# Phi ergo Fibonacci Exploration Resultants

Author: ebuc ,

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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 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 not 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

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

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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

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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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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

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Made some corrections below on 8/26PM
Take note of change below I found a55th #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 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...............................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..................................................20

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

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

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

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

2194843  5..............................................................................8
30 5....................short run.....................................................3
67830022878 5......................................................................12

699782977834784 5..............................................................16
87822891109762 5.................................................................15
003026961 5...........................................................................10
617002 5...................................................................................7
046433824377648610283831268330372429267 5................40 digits
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
2085247

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

And this is kinda of 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 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; #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 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.
6180339887498948482045.........................................................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
3693179318006076672635.......................................................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
88795................................................................................5
44* 5.......................short run...............................................3
474924618 5...........................................................................10
695364864449241044320771344947049 5......................................34
65846788 5.........................................................................9
09874339442212 5..................................................................15
44877066478091 5..................................................................15
88460749988712400765.............................................................20
2170 5.................................................................................5
7 5...........................shortest run.........................................2
179788341662 5.....................................................................13
6249407 5............................................................................8
8906970400028121042762177111777805.......................................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....

991466979873176135...........................................................18
60067087480710131795..............................................................20
236894275...........................................................................9
2194843*  5...........................................................................8
30 5.......................................................................................3
678300228785........................................................................12
699782977834784 5................................................................16
87822891109762 5..................................................................15
003026961 5............................................................................10
6170025................................................................................7
046433824377648610283831268330372429267 5...............................................40
2631165................................................................................7
3392473167111211 5................................................................17
88186385..............................................................................8
133162038400 5........................................................................13
222165..................................................................................6
791286675............................................................................9
29465....................................................................................5
490681131715.........................................................................12
9934323 5..............................................................................8
97349498 5............................................................................9
090409476213222981017261070 5...................................................28
9611645................................................................................7
629909816290  555.......................................................................13,14, and 15th

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In rows #11 and 12, we find a triangle set of 55, 66 and 220.

66 is resultant set of liness-of-relationship between 12 points/nodes.

55 and 220 both divisible by 11 and 5.

We find #5 associations beginging in row #5.  5 - 10 - 10 -5

And in row #6, 7,  8 but at row #9 no numbers are associated with #5 ex none are divisible 5.

After row #9 we find #5 associations in every row.  Apparrently # 9 and 5 are least compatible numbers?