Phi Explorations

[r6r6]

, I take note of the following triple 555's and no 55's { interesting? } ergo the first 555 and all other doubles and triples that occur before 555

..."Leonardo Fibonacci discovered the sequence which converges on phi. In the 1202 AD, Leonardo Fibonacci wrote in his book “Liber Abaci” of a simple numerical sequence that is the foundation for an incredible mathematical relationship behind phi"....

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377

Here as follows is my explorations into phi and my concern specifically is 55, the 11th number on fibonacci line if we start by including zero.

Here below I show the results of my investigations for 55 in the phi number line and what stood out to me is that, a double set of the digits 55 do no occur before we get to a triple set of 555

However, I counted the number of #5 digits before 555 and found there were 54 such #5's. So that is one short of 55 #5's. H,mmm?

11 = 10 of them ---two triple 111's and that is 2nd only to triple 2's---

22 = 10 of them --three triple 2's { we have a winner $$$ }-- the only prime, even number of Universe, is #2

44 = 10 of them -- one triple 4's--

88 = 9 of them ---zero triple 8's

00 = 8 of them --one triple 0's--

33 = 8 of them ---one triple 3's---

66 = 8 of them -- one triple 6's---

77 = 7 of them --how appropriate eh?---- one triple 7's--

99 = 6 of them and --how inappropriate, upside down 6 and 9--- zero triple 9's


1.6180 33 9 88 749894848204586834365638 11 77 20309179805762862135 44 86 22 705260462818902 44 970720720418939 11 374847540 88 07538689175212 66 33 86 222 353693179318 00 607 66 72635 44 333 890865959395829056383 22 66 131 99 28290267 88 06752087 66 8925017 11 69620703 222 104321626954862629631361 44 38149758701 22 0340805 88 795 44 5474924618569536486 444 92410 44 320 77 13 44 9470495658467 88 509874 33 9 44 22 125 44 8 77 0 66 4780915 88 46074 99 88 7124 00 76521705751797 88 341 66 256249407589069704 000 281210427621 77 111 777 805315317141011704 666 5 99 14 66 9798731761356 00 67087480710131795236894275219484353056783 00 22 87856 99 7829 77 8347845878 22 89 11 097625 00 30269615617 00 250464 33 8243 77 648610283831268 33 03724292675263 11 65 33 92473167 111 2 11 5 88 1863851 33 1620384 00 5 222 16579128 66 752946549068 11 31715 99 343235973494985090409476213 222 981017261070596 11 64562 99 09816290 5552085247

[r6r6]

I also take note of a few other interesting findings.



The longest set ---most consecutive set--- of digits, 41, with no doubles occur on line five - six, between 00 and 00.



The longest set --most consecutive set-- of double digits is line four, 77 111 777.



And again, of special note, of all of the numbers, there is no double 55's until we get to 555 on line seven



And out of curosity ---as derived from twin primes in rational whole number line--- I placed in brackets the twin doubles and take note that none of the twins are the same set of digits, except for on line six we have {111 2 11}



Now Phi:

1.6180 {33 9 88} 749894848204586834365638 11 77 20309179805762862135 44 86 22 705260462818902 44 970720720418939 11 374847540 88 07538689175212 66 33 86



222 353693179318 00 607 66 72635 44 333 890865959395829056383 22 66 131 99 28290267 88 06752087 66 8925017 11 69620703 222 104321626954862629631361 44



38149758701 22 0340805 88 795 44 5474924618569536486 444 92410 44 320 77 13 44 9470495658467 88 509874 {33 9 44} 22 125 44 8 {77 0 66} 4780915 88 46074 99



88 7124 00 76521705751797 88 341 66 256249407589069704 000 281210427621 77 111 777 805315317141011704 666 5 99 14 66 9798731761356 00



67087480710131795236894275219484353056783 00 22 87856 99 7829 77 8347845878 {22 89 11} 097625 00 30269615617 00 250464 33 8243 77 648610283831268 33



03724292675263 11 65 33 92473167 {111 2 {11} 5 88} 1863851 33 1620384 00 5 222 16579128 66 752946549068 11 31715 99 343235973494985090409476213 222



981017261070596 11 64562 99 09816290 555 2085247

[r6r6]

There are no sequential double digit #5's, as there is with all of the other numbers 1-9 however, there is 54, #5 digits, before we get to 555. H,mm, now that is interesting.


Special note also on line six of longest set of double-triple digits of similar nature. 77 111 777

[r6r6]

Made some corrections below on 8/26PM
Take note of change below I found a 55th #5 before 555.
.....I take note of the following triple 555's and no 55's { interesting? } ergo the first 555 and all other doubles and triples that occur before 555.......there is 55, #5 digits, before we get to 555. H,mm, now that is interesting.

1.
618033988749894848204 5.........................................22 digits
8683436 5................................................. ...................8 ""
63811772030917980 5................................................. 18
76286213 5................................................. ..................9
44862270 5................................................. .................9
2604628189024497072072041893911374847 5.............38
408807 5................................................. .....................7
3868917 5................................................. ....................8
2126633862223 5................................................. ......14
369317931800607667263 5..........................................22

4433389086 5................................................. ............11
9 5...............................short run....................................2
93958290 5................................................. .................11

63832266131992829026788067 5.................................27
208766892 5................................................. ...............10
01711696207032221043216269 5.................................27
486262963136144381497 5...........................................22
870122034080 5................................................. ..........13

8879 5................................................. ..........................5
44 5..........................short run........................................3
474924618 5................................................. .................10

695364864449241044320771344947049 5.......................34
65846788 5................................................. .....................9
09874339442212 5................................................. ........15
44877066478091 5................................................. ........15
8846074998871240076 5................................................2 0

2170 5................................................. .................................5
7 5...................short run............................................... ........2

179788341662 5................................................. .............13
6249407 5................................................. ............................8

890697040002812104276217711177780 5........................34
31 5................................................. .......................................3
317141011704666 5................................................. ........16

99146697987317613 5................................................. .....18
6006708748071013179 5................................................. ..20
23689427 5................................................. ..........................9

2194843 5................................................. .............................8
30 5
67830022878 5................................................. ................12

699782977834784 5................................................. .........16
87822891109762 5................................................. ...........15
003026961 5................................................. .....................10
617002 5................................................. .................................7
046433824377648610283831268330372429267 5................40
263116 5................................................. ................................7
3392473167111211 5................................................. .........17
8818638 5................................................. ..............................8
133162038400 5................................................. ................13
22216 5................................................. .................................6
79128667 5................................................. ............................9
2946 5................................................. ...................................5 digits
49068113171 5................................................. ....................12
9934323 5................................................. ..............................8
97349498 5................................................. .............................9
090409476213222981017261070 5............................................28
961164 5................................................. ....................................7
629909816290 555............................................... ..13, 14, and 15th
2085247

[r6r6]

'Universe expends energy in two ways. In more frequent little booms, or less frequent big booms'...B Fuller paraphasing



And this is what we see with #55 in my phi explorations.



0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...First 16 Fibonacci numbers with 55 being the 10th if we start with #1.



Made some corrections below on 8/26PM and new findings and formatting 8/29 for easier finding various runs between the #5, which now find on 55 runs before we get to the triple 555 on 56th run



....note-1; of the following triple 555's and whereas we found doubles other numbers from 1-10, we found no 55's { interesting? } i.e. the first set beyond a single #5 is 555.



.....note-2; 31 * 5 * 31 occurs on each side of a #5 on run 33 and 34



.....note-3; run #22 is the only even prime number and 222 is the first triplet to occur and 333 is 2nd triplet, then 444



.....note-4; on first run of 14, we find 6633 preceding 222 and on next run{ 22 } four #3's and 6's we find also the sequence 00 60 '7' 66 which is eerily close to the same sequence in my Pi^3 = 31.00 62 '7' 66...explorations.



Seven{ '7' } 9 digit runs between #5's

Six 8 digit runs

Four 7 digit runs

Three 22 digit runs

Three 15 digit runs

Three 13 digit runs

Three 10 digit runs

Three 3 digit runs

Two 34 digit runs

Two 20 digit runs

Two 18 digit runs

Two 16 digit runs

Two 5 digit runs

One 40 digit run

One 38 digit run

One 14 digit run

One 13 14 and 15th digit run ie..555,

One 11 digit run

One 2 digit run



1.

618033988749894848204 5................................................. ........22 digits includes #5

8683436 5................................................. ......................8 “”

63811772030917980 5................................................. ...........18

76286213 5................................................. ....................9

44862270 5................................................. ....................9

2604628189024497072072041893911374847 5................................38

408807 5................................................. .........................7

3868917 5................................................. .......................8

2126633862223 * 5................................................. ................14

369317931800607667263 5................................................. ......22

4433389086 5................................................. ......................11



9* 5…………….shortest run…………………………...2

93958290 5................................................. ......................9



63832266131992829026788067 5.............................................27

208766892 5................................................. .........................10

01711696207032221043216269 5.............................................27

486262963136144381497 5................................................. ......22

870122034080 5................................................. ....................13

8879 5................................................. ...............................5

44* 5.......................short run............................................... 3

474924618 5................................................. ..........................10

695364864449241044320771344947049 5......................................34

65846788 5................................................. ........................9

09874339442212 5................................................. .................15

44877066478091 5................................................. .................15

8846074998871240076 5................................................. ............20

2170 5................................................. ................................5

7 5...........................shortest run.........................................2

179788341662 5................................................. ....................13

6249407 5................................................. ...........................8

890697040002812104276217711177780 5.......................................34

31* 5.......................short run..............................................3

31*7141011704666 5................................................. .............16

...31 on each side of #5 is reminscent of the 5-fld 31 left and right-skew great planes and bilateral 31 spina nerves....



99146697987317613 5................................................. ..........18

6006708748071013179 5................................................. .............20

23689427 5................................................. ..........................9

2194843* 5................................................. ..........................8

30 5................................................. ......................................3

67830022878 5................................................. .......................12

699782977834784 5................................................. ...............16

87822891109762 5................................................. .................15

003026961 5................................................. ...........................10

617002 5................................................. ...............................7

046433824377648610283831268330372429267 5...............................................40

263116 5................................................. ...............................7

3392473167111211 5................................................. ...............17

8818638 5................................................. .............................8

133162038400 5................................................. .......................13

22216 5................................................. .................................6

79128667 5................................................. ...........................9

2946 5................................................. ...................................5

49068113171 5................................................. ........................12

9934323 5................................................. .............................8

97349498 5................................................. ...........................9

090409476213222981017261070 5................................................. ..28

961164 5................................................. ...............................7

629909816290 555.................................................. .....................13, 14, and 15th

[r6r6]

'Universe expends energy in two ways. In more frequent little booms, or less frequent big booms'...B Fuller paraphasing

And this is what we find with #55 in my phi explorations.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...First 16 Fibonacci numbers with 55 being the 10th if we start with #1.

Made some corrections below on 8/26PM and new findings and formatting 8/29 for easier finding various runs between the #5, which now find on 55 runs before we get to the triple 555 on 56th run

....note-1; of the following triple 555's and whereas we found doubles other numbers from 1-10, we found no 55's { interesting? } i.e. the first set beyond a single #5 is 555.

.....note-2; 31 * 5 * 31 occurs on each side of a #5 on run 33 and 34

.....note-3; run #22 is the only even prime number and 222 is the first triplet to occur and 333 is 2nd triplet, then 444

.....note-4; on first run of 14, we find 6633 preceding 222 and on next run{ 22 } four #3's and 6's we find also the sequence 00 60 '7' 66 which is eerily close to the same sequence in my Pi^3 = 31.00 62 '7' 66...explorations.


Seven{ '7' } 9 digit runs between #5's

Six 8 digit runs

Four 7 digit runs

Three 22 digit runs

Three 15 digit runs

Three 13 digit runs

Three 10 digit runs

Three 3 digit runs

Two 34 digit runs

Two 20 digit runs

Two 18 digit runs

Two 16 digit runs

Two 5 digit runs

One 40 digit run

One 38 digit run

One 14 digit run

One 13 14 and 15th digit run ie..555,

One 11 digit run

One 2 digit run


Next Phi;
1.

618033988749894848204 5................................................. ........22 digits includes #5

8683436 5................................................. ......................8 “”

63811772030917980 5................................................. ...........18

76286213 5................................................. ....................9

44862270 5................................................. ....................9

2604628189024497072072041893911374847 5................................38

408807 5................................................. .........................7

3868917 5................................................. .......................8

2126633862223 * 5................................................. ................14

369317931800607667263 5................................................. ......22

4433389086 5................................................. ......................11



9* 5…………….shortest run…………………………...2

93958290 5................................................. ......................9



63832266131992829026788067 5.............................................27

208766892 5................................................. .........................10

01711696207032221043216269 5.............................................27

486262963136144381497 5................................................. ......22

870122034080 5................................................. ....................13

8879 5................................................. ...............................5

44* 5.......................short run............................................... 3

474924618 5................................................. ..........................10

695364864449241044320771344947049 5......................................34

65846788 5................................................. ........................9

09874339442212 5................................................. .................15

44877066478091 5................................................. .................15

8846074998871240076 5................................................. ............20

2170 5................................................. ................................5

7 5...........................shortest run.........................................2

179788341662 5................................................. ....................13

6249407 5................................................. ...........................8

890697040002812104276217711177780 5.......................................34

31* 5.......................short run..............................................3

31*7141011704666 5................................................. .............16

...31 on each side of #5 is reminscent of the 5-fld 31 left and right-skew great planes and bilateral 31 spina nerves....



99146697987317613 5................................................. ..........18

6006708748071013179 5................................................. .............20

23689427 5................................................. ..........................9

2194843* 5................................................. ..........................8

30 5................................................. ......................................3

67830022878 5................................................. .......................12

699782977834784 5................................................. ...............16

87822891109762 5................................................. .................15

003026961 5................................................. ...........................10

617002 5................................................. ...............................7

046433824377648610283831268330372429267 5...............................................40

263116 5................................................. ...............................7

3392473167111211 5................................................. ...............17

8818638 5................................................. .............................8

133162038400 5................................................. .......................13

22216 5................................................. .................................6

79128667 5................................................. ...........................9

2946 5................................................. ...................................5

49068113171 5................................................. ........................12

9934323 5................................................. .............................8

97349498 5................................................. ...........................9

090409476213222981017261070 5................................................. ..28

961164 5................................................. ...............................7

629909816290 555.................................................. .....................13, 14, and 15th

[r6r6]

Ok, correcting previous errors and adding new info. Record of it as you go through the list.

1} I found two more #5's so that is total of 57, #5's and not 55, #5's as I had previusly reported.


2} What has not changed is there is not sequential double set of 55's before triplet 555.


3} Ive added in the the finding of the first sequential set of 55 at bottom of this list below.

1.

618033988749894848204 5................................................. ........22 digits includes #5

8683436 5................................................. ......................8 “”

638117720309179805................................ ............................18

76286213 5................................................. ....................9

44862270 5................................................. ....................9

2604628189024497072072041893911374847 5................................38

408807 5................................................. .........................7

3868917 5................................................. .......................8

2126633862223 5................................................. ................14

3693179318006076672635............................ ...........................22

4433389086 5................................................. ......................11

9 5…………….shortest run…………………………...2

939 5…oops, discovered another #5 so it makes 56 #5’s before the triplet 555

…this latter discovered 9/20/20……

8290 5................................................. ......................9

63832266131992829026788067 5.............................................27

208766892 5................................................. .........................10

01711696207032221043216269 5.............................................27

486262963136144381497 5................................................. ......22

870122034080 5................................................. ....................13

8879 5................................................. ...............................5

44 5.......................short run............................................... 3

474924618 5................................................. ..........................10

695364864449241044320771344947049 5......................................34

6 5…oops another #5 discovered here on same day so that is 57 #5’s before 555 triplet

….discovered 9/20/20….

846788 5................................................. ........................9

09874339442212 5................................................. .................15

44877066478091 5................................................. .................15

8846074998871240076 5................................................. ............20

2170 5................................................. ................................5

7 5...........................shortest run.........................................2

179788341662 5................................................. ....................13

6249407 5................................................. ...........................8

890697040002812104276217711177780 5.......................................34

31 5......................32nd run is a short run...........................3

317141011704666 5................................................. .............16

...above takenote that 31 on each side of #5 is reminscent of the 5-fold 31 left and right-skew great planes and bilateral 31 spinal nerves....

99146697987317613 5................................................. ..........18

6006708748071013179 5................................................. .............20

23689427 5................................................. ..........................9

21948435.......................................... .................................8

30 5................................................. ......................................3

67830022878 5................................................. .......................12

699782977834784 5................................................. ...............16

87822891109762 5................................................. .................15

003026961 5................................................. ...........................10

617002 5................................................. ...............................7

046433824377648610283831268330372429267 5...............................................40

263116 5................................................. ...............................7

3392473167111211 5................................................. ...............17

8818638 5................................................. .............................8

133162038400 5................................................. .......................13

22216 5................................................. .................................6

79128667 5................................................. ...........................9

2946 5................................................. ...................................5

49068113171 5................................................. ........................12

9934323 5................................................. .............................8

97349498 5................................................. ...........................9

090409476213222981017261070 5................................................. ..28

961164 5................................................. ...............................7

629909816290 555............................................... ........................13,14, and 15th.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Continuing below, with phi, from where we stopped above, with the 555 triplet.

208 5

247903 5

240602017279974717 5

342777 5

9277862 5

6194320827 5

0 5

1312181 5

...this totals 65 #5's before we get to the first double 55 numerical set.



628 55… and here we find our first double set of integers #5.

As I'm always on look out of cosmic 66's ---see my Pi-Time 66.4---, I take note of the 66th #5 being in the first double set 55 in Phi.

[RuberPeach]

someone met me today and was sharpening a knife by and electricity pole and was hearing "I am going to cut your throat"
On the end of the road was a bridge over a river. Bridge doesn't cut river.As for the food issue I was having a juice in the backpack.
3 dogs didn't want me to continue my journey. 3 loose dogs on the street. Dangerous barking

[r6r6]

The Infinite Pattern LINK

https://www.youtube.com/watch?v=48sC...RPpshn6CB9y2**

Above we find phi and fibonacci in regards to Penrose tilings and quasi-crystals and 5-fold symmetrys. Below I look for numerical patterns with numerical phi.

1.

618033988749894848204 5................................................. ........22 digits includes #5

8683436 5................................................. ......................8 “”

638117720309179805................................ ............................18

76286213 5................................................. ....................9

44862270 5................................................. ....................9

2604628189024497072072041893911374847 5................................38

408807 5................................................. .....................7

3868917 5................................................. .......................8

2126633862223 5................................................. ................14

3693179318006076672635............................ ...........................22

4433389086 5................................................. ......................11

9 5……………..............………………� �………...2

939 5….............................................. ......4

8290 5................................................. ......................9

63832266131992829026788067 5.............................................27

208766892 5................................................. .........................10

01711696207032221043216269 5.............................................27

486262963136144381497 5................................................. ......22

870122034080 5................................................. ....................13

8879 5................................................. .......................5

44 5................................................. ...................3

474924618 5................................................. ......................10
695364864449241044320771344947049 5......................................34

6 5................................................. ..............2

846788 5................................................. ........................9

09874339442212 5................................................. .................15

44877066478091 5................................................. .................15

8846074998871240076 5................................................. ............20

2170 5................................................. ...........................5

7 5................................................. ................2

179788341662 5................................................. ....................13

6249407 5................................................. ...........................8

890697040002812104276217711177780 5.......................................34

31 5......................32nd run is a short run...........................3

317141011704666 5................................................. .............16

...above tak enote that 31 on each side of #5 is reminscent of the 5-fold 31 left and right-skew great planes and bilateral 31 spinal nerves....

99146697987317613 5................................................. ..........18

6006708748071013179 5................................................. .............20

23689427 5................................................. .....................9

21948435.......................................... ...........................8

30 5................................................. ........3

67830022878 5................................................. .......................12

699782977834784 5................................................. ...............16

87822891109762 5................................................. .................15

003026961 5................................................. ...........................10

617002 5................................................. ...............................7

046433824377648610283831268330372429267 5...............................................40

263116 5................................................. ...............................7

3392473167111211 5................................................. ...............17

8818638 5................................................. .............................8

133162038400 5................................................. .......................13

22216 5................................................. .................................6

79128667 5................................................. ...........................9

2946 5................................................. ...................................5

49068113171 5................................................. ........................12

9934323 5................................................. .............................8

97349498 5................................................. ...........................9

090409476213222981017261070 5................................................. ..28

961164 5................................................. ...............................7

629909816290 555............................................... ........................13,14, and 15th triplet set of 555

208 5................................4

247903 5................................................. ................................7

240602017279974717 5................................................. ..................19

342777 5................................................. .................................7

9277862 5................................................. .................................8

6194320827 5................................................. .................................11

0 5.....................2

1312181 5................................................. ................................8
...this totals 65 #5's, before we get to the first double set #5's.

628 55…....................................4
and here we find our first double set of integers #5.

As I'm always on look out of cosmic 66's ---see my Pi-Time 66.4---, I take note of the above first set of #5's occurring at the 66th and 67th position in phi, if we do not include the previous triplet 555.

[r6r6]

https://www.cut-the-knot.org/arithme...InPascal.shtml

Ive been interested in Pascals numerical triangle for various reasons;

1} close-packing of spheres as found in B Fullers Synergetics and specifically with the cubo-octahedron aka Vector Equlirbrium { VE }, LINK

2} triangular cluster of 55 { Phi }, 66 { Pi-associated }, 220 on the 11th and 12th frequency, and,

......2a} 20 { Pi-associated and VE and Icosahedron } on the 6th frequency.

...."A different sort of presence of π was discovered by Jonas Castillo Toloza in 2007; this one associated with the triangular numbers:"

As seen in the link at top of this page.


On this above page, the first thing that stands out to me, is that the numerical 20 is at nuclear location, related to the triangular set and that is the only nuclear location in this set, as presribed by the linear following of Pi associations.


The non-nucleated, 5-fold icosahedron { 12 vertexes } has 20 surface equaliteral triangles, and the 4-fold VE { 12 vertexes } --in Synergetics--- has a tetrahedron volume of 20.