Collapse, then double
Hello Math-Fun,
I’m
looking for loops with the hereunder rules:
-start with a(1)
-if a substring of a(1)
is made of identical digits, replace the said substring with the sum of its
digits
-iterate until there are no more substrings
with identical digits in a(1)
-double a(1) and
start the procedure again.
Ex.
a(1)=55027771
a(1)=1002211
a(1)=1042
a(2)=2084
a(3)=4168
a(4)=8336
a(4)=866
a(4)=812
a(5)=1624
etc.
18
enters in the loop 18-36-72-144-(18)
Best,
É.
__________
[Allan
Wechsler]:
If I understand you correctly, you are defining
a function C(n) (C stands for "collapse"), which replaces runs of
consecutive identical digits by their sum; then you define D(n) as n (if n ==
C(n)) and D(C(n)) otherwise -- in other words, keep applying C until the result
stops changing. Your overall question is about the dynamics of E(n) = D(2n).
If that’s correct, then I think 178 is the
smallest element of a 24-step loop. I did that by hand. For some reason I keep
making stupid mistakes trying to code this.
[Hans Havermann]:
On Tue, Jun 5, 2012 at 3:50 AM, Eric Angelini
wrote:
> 18 enters in the loop 18-36-72-144-(18)
A small quibble:
Since the doubling appears to be part of
"the procedure", I make that: 18, 36, 72, 144, 36,
..., so I would represent the loop portion as {36, 72, 144}, putting the
smallest member of the loop first. There are loop members, and loop precursors
that run into loops, and I take 18 as one of the latter.
Trivially, I
think we can add a zero to the end of each member of a loop to turn it a new
loop; for example, {360, 720, 1440}.
So far, I have nine
non-trivial loops (assuming that I have done things correctly) and put them here.
They are introduced by [smallest
precursor, loop length].
Additionally, I have marked the largest loop member with an asterisk (*).
[1,
24]: {356, 712, 1424, 2848, 5696,
11392, 4784, 9568, 19136, 38272, 76544, 15316, 30632, 61264, *122528, 29056, 58112, 1168, 536, 1072,
2144, 436, 872, 1744}
[3,
66]: {492, 984, 1968, 3936, 7872,
15744, 3156, 6312, 12624, 25248, 50496, 100992, 20364, 40728, 81456, 162912,
325824, 651648, 1303296, 2606592, 5213184, 10426368, 20852736, 41705472, *83410944, 16682196, 964392, 1928784,
3857568, 7715136, 2830272, 5660544, 1024116, 204852, 409704, 819408, 1638816,
3263232, 6526464, 13052928, 26105856, 52211712, 1085424, 2170848, 4341696,
8683392, 1737384, 3474768, 6949536, 13899072, 27636144, 5527236, 2054472,
411744, 8556, 16212, 32424, 64848, 129696, 259392, 518784, 1037568, 2075136,
4150272, 8300544, 166116}
[9,
3]: {36, 72, *144}
[27,
86]: {756, 1512, 3024, 6048, 12096,
24192, 48384, 96768, 193536, 387072, 774144, 3636, 7272, 14544, 2916, 5832,
11664, 4248, 8496, 16992, 32364, 64728, 129456, 258912, 517824, 1035648, 2071296,
4142592, 8285184, 16570368, *33140736,
12281472, 2962944, 592596, 1185192, 570384, 1140768, 481536, 963072, 1926144,
385236, 770472, 280944, 56196, 112392, 8784, 17568, 35136, 70272, 140544,
28116, 5652, 11304, 4608, 9216, 18432, 36864, 73728, 147456, 294912, 589824,
1179648, 559296, 218592, 437184, 874368, 1748736, 3497472, 6994944, 1236996,
2472372, 4944744, 99756, 37512, 75024, 150048, 30096, 6192, 12384, 24768,
49536, 99072, 36144, 7236, 14472, 3744}
[129,
122]: {1956, 3912, 7824, 15648, 31296,
62592, 125184, 250368, 500736, 101472, 202944, 40596, 81192, 16584, 33168,
12336, 2424, 4848, 9696, 19392, 38784, 77568, 29136, 58272, 116544, 5316,
10632, 21264, 42528, 85056, 170112, 3408, 6816, 13632, 27264, 54528, 109056,
218112, 4368, 8736, 17472, 34944, 6996, 12372, 24744, 4956, 9912, 3624, 7248,
14496, 3792, 7584, 15168, 30336, 6024, 12048, 24096, 48192, 96384, 192768,
385536, 762072, 1524144, 304836, 609672, 1219344, 243876, 487752, 962904,
1925808, 3851616, 7703232, 2806464, 5612928, 11225856, 491712, 983424, 1966848,
3825696, 7651392, 15302784, 30605568, 61202136, *122404272, 3608544, 721716, 1443432, 366864, 625728, 1251456,
2502912, 5005824, 1011648, 205296, 410592, 821184, 16968, 33936, 13872, 27744,
4296, 8592, 17184, 34368, 68736, 137472, 274944, 54996, 108372, 216744, 43356,
9312, 18624, 37248, 74496, 15792, 31584, 63168, 126336, 2436, 4872, 9744}
[513,
22]: {37296, 74592, 149184, 298368,
596736, *1193472, 586944, 117396, 54792,
109584, 219168, 438336, 87624, 175248, 350496, 700992, 140364, 280728, 561456,
1122912, 49824, 99648}
[873,
18]: {3492, 6984, 13968, 27936,
55872, 21744, 4356, 8712, 17424, 34848, 69696, 139392, 278784, 557568, 215136,
430272, *860544, 172116}
[2367,
153]: {15156, 30312, 60624, 121248,
242496, 484992, 968364, 1936728, 3873456, 7746912, 373824, 747648, 1495296,
2990592, 4361184, 872568, 1745136, 3490272, 6980544, 1396116, 279252, 558504,
217008, 43416, 86832, 173664, 346248, 692496, 1384992, 2768364, 5536728,
2073456, 4146912, 8293824, 16587648, 33175296, 12350592, 24701184, 4940568,
9881136, 1832472, 3664944, 624996, 1248372, 2496744, 499356, 836712, 1673424,
3346848, 1293696, 2587392, 5174784, 10349568, 20699136, 41236272, 82472544,
16494516, 32989032, 65978064, 131956128, 263912256, 52782912, 105565824,
202131648, 404263296, 808526592, 1617053184, 3234106368, 6468212736,
12936425472, 25872850944, 5174570196, 10349140392, 20698280784, 41396561568,
82793123136, 165586246272, *322172492544,
6834498516, 1367797032, 2722994064, 548368128, 1096736256, 2193472512,
4386945024, 8773890048, 1628778096, 3256296192, 6512592384, 13025184768,
26050369536, 52100739072, 10421478144, 2084295636, 4168591272, 8337182544,
173436516, 346873032, 693746064, 1387492128, 2774984256, 437968512, 875937024,
1751874048, 3503748096, 7007496192, 1414992384, 2828364768, 5656729536,
11313459072, 4626918144, 925383636, 1850767272, 3701534544, 740306916,
1480613832, 2961227664, 592294248, 118988496, 57832992, 115664364, 50248728, 100497456,
20994912, 40369824, 80739648, 161479296, 322958592, 69917184, 123634368,
247268736, 494537472, 989074944, 197814996, 395628372, 791256744, 158251356,
316502712, 633005424, 2410848, 4821696, 9643392, 1929384, 3858768, 7717536,
2835072, 5670144, 1134036, 468072, 936144, 187236, 374472, 75744}
[42891,
18]: {817032, 1634064, 3268128,
6536256, 13072512, 26145024, 52290048, 1098096, 2196192, 4392384, 8784768,
17569536, 35139072, *70278144,
14055636, 28021272, 56042544, 11208516}
[1235349, 14]: {9162792, 18325584, 36642168, 62484336, 12496824, 24993648,
48367296, 96734592, 193469184, 386938368, *773876736,
287753472, 562906944, 112581396}
__________
[Hans]:
I’ve found two more
loops. They are, surprisingly, in resonance with each other, sharing the last
8/9 digits:
[?, 18]: {409642128, 819284256, 1638568512, 3277137024, 6428274048, 12856548096, 25713096192, 51426192384, 102852384768, 205704769536, *411409539072, 84819078144, 16963815636, 33927631272, 13855262544, 2762052516, 5524105032, 2048210064}
[?, 18]: {609642128, 1219284256, 2438568512, 4877137024, 9628274048, 19256548096, 38513096192, 77026192384, 28052384768, 56104769536, *112209539072, 4819078144, 963815636, 1927631272, 3855262544, 762052516, 1524105032, 3048210064}
__________
[Jean-Marc Falcoz]:
J’ai fait un programme qui donne une liste des
valeurs et en tire un graphe orienté, MAIS... les nombres deviennent vite très
grands, et les chaînes très longues. Par exemple, la chaîne associée au nombre
de départ 3 est
longue de plus de 400 termes :
{3, 6, 12, 24, 48, 96,
192, 384, 768, 1536, 3072, 6144, 618, 1236, 2472, 4944, 498, 996, 186, 372,
744, 78, 156, 312, 624, 1248, 2496, 4992, 4182, 8364, 16728, 33456, 6456,
12912, 25824, 51648, 103296, 206592, 413184, 826368, 1652736, 3305472, 605472,
1210944, 121098, 242196, 484392, 968784, 1937568, 3875136, 7750272, 1450272,
2900544, 29058, 58116, 5826, 11652, 2652, 5304, 10608, 21216, 42432, 84864, 169728,
339456, 69456, 138912, 277824, 214824, 429648, 859296, 1718592, 3437184,
6874368, 13748736, 27497472, 54994944, 5418498, 10836996, 10836186, 21672372,
43344744, 46878, 93756, 187512, 375024, 750048, 75048, 150096, 15096, 30192,
60384, 120768, 241536, 483072, 966144, 91218, 182436, 364872, 729744, 72978,
145956, 291912, 583824, 1167648, 267648, 535296, 1070592, 2141184, 214284,
428568, 857136, 1714272, 3428544, 342858, 685716, 1371432, 2742864, 5485728, 10971456,
21942912, 43885824, 43165824, 86331648, 8661648, 8121648, 16243296, 32486592,
64973184, 129946368, 121846368, 243692736, 487385472, 974770944, 97414098,
194828196, 389656392, 779312784, 149312784, 298625568, 298621068, 597242136,
1194484272, 29884272, 29164272, 58328544, 5832858, 11665716, 2125716, 4251432,
8502864, 17005728, 1705728, 3411456, 342456, 684912, 1369824, 2739648, 5479296,
10958592, 21917184, 43834368, 87668736, 87128736, 174257472, 348514944,
34851498, 69702996, 69702186, 139404372, 278808744, 27160878, 54321756,
108643512, 217287024, 434574048, 869148096, 1738296192, 3476592384, 6953184768,
13906369536, 27812739072, 55625478144, 1062547818, 2125095636, 4250191272,
8500382544, 85038258, 170076516, 17076516, 34153032, 68306064, 136612128, 131212128,
262424256, 524848512, 1049697024, 2099394048, 2018394048, 4036788096,
4036716096, 8073432192, 16146864384, 32293728768, 3493728768, 6987457536,
13974915072, 27949830144, 2794983018, 5589966036, 1081812036, 2163624072,
4327248144, 432724818, 865449636, 86589636, 173179272, 346358544, 34635858,
69271716, 138543432, 277086864, 214086864, 428173728, 856347456, 1712694912,
3425389824, 6850779648, 6850149648, 13700299296, 1370218296, 2740436592, 5480873184,
10961746368, 21923492736, 43846985472, 87693970944, 8769397098, 17538794196,
35077588392, 35014516392, 70029032784, 7029032784, 14058065568, 14058061068,
28116122136, 282614136, 565228272, 56548272, 113096544, 2309658, 4619316,
9238632, 18477264, 18414264, 36828528, 73657056, 147314112, 14731422, 1473144,
147318, 294636, 589272, 1178544, 27858, 55716, 10716, 21432, 42864, 85728, 171456,
342912, 685824, 1371648, 2743296, 5486592, 10973184, 21946368, 43892736,
87785472, 81485472, 162970944, 16297098, 32594196, 65188392, 65116392, 6526392,
13052784, 26105568, 26101068, 52202136, 5402136, 10804272, 21608544, 2160858,
4321716, 8643432, 17286864, 34573728, 69147456, 138294912, 276589824,
553179648, 103179648, 206359296, 412718592, 825437184, 1650874368, 3301748736, 601748736,
1203497472, 2406994944, 240618498, 481236996, 481236186, 962472372, 1924944744,
19249878, 38499756, 38418756, 76837512, 153675024, 307350048, 30735048,
61470096, 6147096, 12294192, 1494192, 2988384, 2916384, 5832768, 11665536,
2121036, 4242072, 8484144, 848418, 1696836, 3393672, 693672, 1387344, 138738,
277476, 214476, 21876, 43752, 87504, 175008, 17508, 35016, 70032, 7032, 14064,
28128, 56256, 112512, 22512, 4512, 9024, 18048, 36096, 72192, 144384, 18384, 36768,
73536, 147072, 294144, 29418, 58836, 51636, 103272, 206544, 20658, 41316,
82632, 165264, 330528, 60528, 121056, 242112, 24222, 246, 492, 984, 1968, 3936, 7872, 15744,
1578, 3156, 6312, 12624, 25248, 50496, 100992, 10182, 20364, 40728, 81456,
162912, 325824, 651648, 1303296, 2606592, 5213184, 10426368, 20852736,
41705472, 83410944, 8341098, 16682196, 11282196, 2282196, 482196, 964392, 1928784,
3857568, 7715136, 1415136, 2830272, 5660544, 512058, 1024116, 102426, 204852,
409704, 819408, 1638816, 1631616, 3263232, 6526464, 13052928, 26105856,
52211712, 542712, 1085424, 2170848, 4341696, 8683392, 868692, 1737384, 3474768,
6949536, 13899072, 13818072, 27636144, 2763618, 5527236, 1027236, 2054472,
205872, 411744, 4278, 8556, 8106, 16212, 32424, 64848, 129696, 259392, 518784,
1037568, 2075136, 4150272, 8300544, 83058, 166116, 11226, 246, ... et
ça boucle}
Chaque entier de 1 à 50000 finit sur une des boucles
suivantes (classées d’après le plus petit élément de la boucle) :
{18, 36, 72, 144, 18} longueur 4 (et bien sûr {180, 360, 720, 1440, 180})
{178, 356, 712, 1424, 2848, 5696, 11392, 2392, 4784, 9568, 19136,
38272, 76544, 7658, 15316, 30632, 61264, 122528, 14528, 29056, 58112, 5822, 584,
1168, 268, 536, 1072, 2144, 218, 436, 872, 1744, 178} longueur 32 (et {1780, ...}
{246, 492, 984, 1968, 3936, 7872, 15744, 1578, 3156, 6312, 12624,
25248, 50496, 100992, 10182, 20364, 40728, 81456, 162912, 325824, 651648, 1303296,
2606592, 5213184, 10426368, 20852736, 41705472, 83410944, 8341098, 16682196, 11282196,
2282196, 482196, 964392, 1928784, 3857568, 7715136, 1415136, 2830272, 5660544, 512058,
1024116, 102426, 204852, 409704, 819408, 1638816, 1631616, 3263232, 6526464, 13052928,
26105856, 52211712, 542712, 1085424, 2170848, 4341696, 8683392, 868692, 1737384,
3474768, 6949536, 13899072, 13818072, 27636144, 2763618, 5527236, 1027236, 2054472,
205872, 411744, 4278, 8556, 8106, 16212, 32424, 64848, 129696, 259392, 518784, 1037568,
2075136, 4150272, 8300544, 83058, 166116, 11226, 246} longueur 87 (et {2460, ...})
{378, 756, 1512, 3024, 6048, 12096, 24192, 48384, 96768, 193536,
387072, 774144, 14418, 1818, 3636, 7272, 14544, 1458, 2916, 5832, 11664, 2124, 4248,
8496, 16992, 16182, 32364, 64728, 129456, 258912, 517824, 1035648, 2071296, 4142592,
8285184, 16570368, 33140736, 6140736, 12281472, 1481472, 2962944, 296298, 592596,
1185192, 285192, 570384, 1140768, 240768, 481536, 963072, 1926144, 192618, 385236,
770472, 140472, 280944, 28098, 56196, 112392, 22392, 4392, 8784, 17568, 35136, 70272,
140544, 14058, 28116, 2826, 5652, 11304, 2304, 4608, 9216, 18432, 36864, 73728,
147456, 294912, 589824, 1179648, 279648, 559296, 109296, 218592, 437184, 874368,
1748736, 3497472, 6994944, 618498, 1236996, 1236186, 2472372, 4944744, 49878, 99756,
18756, 37512, 75024, 150048, 15048, 30096, 3096, 6192, 12384, 24768, 49536, 99072,
18072, 36144, 3618, 7236, 14472, 1872, 3744, 378} longueur 116
(et...)
{978, 1956, 3912, 7824, 15648, 31296, 62592, 125184, 250368, 500736,
50736, 101472, 202944, 20298, 40596, 81192, 8292, 16584, 33168, 6168, 12336, 1266,
1212, 2424, 4848, 9696, 19392, 38784, 77568, 14568, 29136, 58272, 116544, 2658,
5316, 10632, 21264, 42528, 85056, 170112, 17022, 1704, 3408, 6816, 13632, 27264,
54528, 109056, 218112, 21822, 2184, 4368, 8736, 17472, 34944, 3498, 6996, 6186,
12372, 24744, 2478, 4956, 9912, 1812, 3624, 7248, 14496, 1896, 3792, 7584, 15168,
30336, 3066, 3012, 6024, 12048, 24096, 48192, 96384, 192768, 385536, 381036, 762072,
1524144, 152418, 304836, 609672, 1219344, 121938, 243876, 487752, 481452, 962904,
1925808, 3851616, 7703232, 1403232, 2806464, 5612928, 11225856, 245856, 491712,
983424, 1966848, 1912848, 3825696, 7651392, 15302784, 30605568, 30601068, 61202136,
122404272, 14404272, 1804272, 3608544, 360858, 721716, 1443432, 183432, 366864,
312864, 625728, 1251456, 2502912, 5005824, 505824, 1011648, 102648, 205296, 410592,
821184, 82284, 8484, 16968, 33936, 6936, 13872, 27744, 2148, 4296, 8592, 17184,
34368, 68736, 137472, 274944, 27498, 54996, 54186, 108372, 216744, 21678, 43356,
4656, 9312, 18624, 37248, 74496, 7896, 15792, 31584, 63168, 126336, 12666, 1218,
2436, 4872, 9744, 978}
longueur 168 (et...)
{1746, 3492, 6984, 13968, 27936, 55872, 10872, 21744, 2178, 4356,
8712, 17424, 34848, 69696, 139392, 278784, 557568, 107568, 215136, 430272, 860544,
86058, 172116, 17226, 1746}
longueur 24
(et...)
{7578, 15156, 30312, 60624, 121248, 242496, 484992, 484182, 968364,
1936728, 3873456, 7746912, 1446912, 186912, 373824, 747648, 1495296, 2990592, 2180592,
4361184, 436284, 872568, 1745136, 3490272, 6980544, 698058, 1396116, 139626, 279252,
558504, 108504, 217008, 21708, 43416, 86832, 173664, 173124, 346248, 692496, 1384992,
1384182, 2768364, 5536728, 1036728, 2073456, 4146912, 8293824, 16587648, 33175296,
6175296, 12350592, 24701184, 2470284, 4940568, 9881136, 916236, 1832472, 3664944,
312498, 624996, 624186, 1248372, 2496744, 249678, 499356, 418356, 836712, 1673424,
3346848, 646848, 1293696, 2587392, 5174784, 10349568, 20699136, 20618136, 41236272,
82472544, 8247258, 16494516, 32989032, 65978064, 131956128, 263912256, 26391456,
52782912, 105565824, 101065824, 202131648, 404263296, 808526592, 1617053184, 3234106368,
6468212736, 12936425472, 25872850944, 2587285098, 5174570196, 10349140392, 20698280784,
41396561568, 82793123136, 165586246272, 161086246272, 322172492544, 3417249258,
6834498516, 683898516, 1367797032, 1361497032, 2722994064, 274184064, 548368128,
1096736256, 2193472512, 4386945024, 8773890048, 814389048, 1628778096, 1628148096,
3256296192, 6512592384, 13025184768, 26050369536, 52100739072, 5210739072, 10421478144,
1042147818, 2084295636, 4168591272, 8337182544, 86718258, 173436516, 346873032,
693746064, 1387492128, 2774984256, 2144984256, 218984256, 437968512, 875937024,
1751874048, 3503748096, 7007496192, 707496192, 1414992384, 1414182384, 2828364768,
5656729536, 11313459072, 2313459072, 4626918144, 462691818, 925383636, 1850767272,
3701534544, 370153458, 740306916, 1480613832, 2961227664, 296147124, 592294248,
59494248, 118988496, 28916496, 57832992, 57832182, 115664364, 25124364, 50248728,
100497456, 10497456, 20994912, 20184912, 40369824, 80739648, 161479296, 322958592,
34958592, 69917184, 61817184, 123634368, 247268736, 494537472, 989074944, 98907498,
197814996, 197814186, 395628372, 791256744, 79125678, 158251356, 316502712, 633005424,
6605424, 1205424, 2410848, 4821696, 9643392, 964692, 1929384, 3858768, 7717536,
1417536, 2835072, 5670144, 567018, 1134036, 234036, 468072, 936144, 93618, 187236,
374472, 37872, 75744, 7578}
longueur 216 (et...)
{18648, 37296, 74592, 149184, 298368, 596736, 1193472, 293472,
586944, 58698, 117396, 27396, 54792, 109584, 219168, 438336, 43866, 43812, 87624,
175248, 350496, 700992, 70182, 140364, 280728, 561456, 1122912, 24912, 49824, 99648,
18648} longueur 30 (et...)
{408516, 817032, 1634064, 3268128, 6536256, 13072512, 26145024,
52290048, 549048, 1098096, 2196192, 4392384, 8784768, 17569536, 35139072, 70278144,
7027818, 14055636, 14010636, 28021272, 56042544, 5604258, 11208516, 2208516, 408516} longueur 24 (et
...)
De plus, pour les nombres < 100000, j’ai regardé
quel était le plus long trajet total (y compris la boucle finale parcourue une
seule fois) ; le vainqueur est 53269, avec un trajet de longueur 864 (avec terme minimum = 46 et terme
maximum = 521448580768) :
{53269, 106538,
213076, 426152, 852304, 1704608, 3409216, 6818432, 13636864, 27273728, 54547456,
109094912, 218189824, 436379648, 872759296, 1745518592, 1741018592, 3482037184,
6964074368, 13928148736, 27856297472, 55712594944, 1071259498, 2142518996, 2142518186,
4285036372, 8570072744, 85707278, 171414556, 171414106, 342828212, 685656424, 1371312848,
2742625696, 5485251392, 10970502784, 21941005568, 2194101068, 4388202136, 4316202136,
8632404272, 17264808544, 1726480858, 3452961716, 6905923432, 13811846864, 1382846864,
2765693728, 5531387456, 1031387456, 2062774912, 2062144912, 206218912, 412437824,
824875648, 1649751296, 3299502592, 3218502592, 6437005184, 643705184, 1287410368,
2574820736, 5149641472, 10299282944, 1021828298, 2043656596, 4087313192, 8174626384,
16349252768, 32698505536, 32698501036, 65397002072, 6539702072, 13079404144, 1307940418,
2615880836, 2615160836, 5230321672, 10460643344, 104606468, 209212936, 418425872,
836851744, 83685178, 167370356, 334740712, 64740712, 129481424, 258962848, 517925696,
1035851392, 2071702784, 4143405568, 4143401068, 8286802136, 16573604272, 33147208544,
614720858, 1229441716, 14981716, 29963432, 21863432, 43726864, 87453728, 174907456,
349814912, 699629824, 618629824, 1237259648, 2474519296, 4949038592, 9898077184,
9898014184, 19796028368, 39592056736, 79184113472, 7918423472, 15836846944, 1583684698,
3167369396, 6334738792, 664738792, 124738792, 249477584, 249414584, 498829168, 491629168,
983258336, 98325866, 98325812, 196651624, 191251624, 382503248, 765006496, 76506496,
153012992, 153012182, 306024364, 612048728, 1224097456, 144097456, 18097456, 36194912,
72389824, 144779648, 18149648, 36299296, 36218296, 72436592, 144873184, 18873184,
11673184, 2673184, 5346368, 10692736, 21385472, 42770944, 4214098, 8428196, 16856392,
33712784, 6712784, 13425568, 13421068, 26842136, 53684272, 107368544, 10736858,
21473716, 42947432, 85894864, 171789728, 343579456, 687158912, 1374317824, 2748635648,
5497271296, 10994542592, 10184542592, 20369085184, 40738170368, 81476340736, 162952681472,
325905362944, 32590536298, 65181072596, 130362145192, 260724290384, 521448580768,
52188580768, 52116580768, 5226580768, 546580768, 1093161536, 2186323072, 4372646144,
437264618, 874529236, 1749058472, 3498116944, 34982698, 69965396, 61865396, 123730792,
247461584, 494923168, 989846336, 98984666, 9898418, 19796836, 39593672, 79187344,
7918738, 15837476, 31674952, 63349904, 6641804, 1241804, 2483608, 4967216, 9934432,
183832, 367664, 367124, 734248, 1468496, 2936992, 2936182, 5872364, 11744728, 278728,
557456, 107456, 214912, 429824, 859648, 1719296, 3438592, 6877184, 6814184, 13628368,
27256736, 54513472, 109026944, 10902698, 21805396, 43610792, 87221584, 8741584,
17483168, 34966336, 3491266, 3491212, 6982424, 13964848, 27929696, 55859392, 10859392,
21718784, 43437568, 86875136, 173750272, 347500544, 3475058, 6950116, 695026, 1390052,
139052, 278104, 556208, 106208, 212416, 424832, 849664, 849124, 1698248, 3396496,
696496, 1392992, 1392182, 2784364, 5568728, 1068728, 2137456, 4274912, 8549824,
17099648, 17018648, 34037296, 68074592, 136149184, 272298368, 27498368, 54996736,
54186736, 108373472, 216746944, 21674698, 43349396, 4649396, 9298792, 18597584,
37195168, 74390336, 7439066, 7439012, 14878024, 29756048, 59512096, 119024192, 29024192,
58048384, 116096768, 26096768, 52193536, 104387072, 208774144, 20814418, 2081818,
4163636, 8327272, 16654544, 1125458, 225458, 45458, 90916, 181832, 363664, 363124,
726248, 1452496, 2904992, 2904182, 5808364, 11616728, 2616728, 5233456, 526456,
1052912, 2105824, 4211648, 422648, 44648, 8648, 17296, 34592, 69184, 138368, 276736,
553472, 103472, 206944, 20698, 41396, 82792, 165584, 161084, 322168, 34168, 68336,
6866, 6812, 13624, 27248, 54496, 5896, 11792, 2792, 5584, 1084, 2168, 4336, 466,
412, 824, 1648, 3296, 6592, 13184, 26368, 52736, 105472, 210944, 21098, 42196, 84392,
168784, 337568, 67568, 135136, 270272, 540544, 54058, 108116, 10826, 21652, 43304,
4604, 9208, 18416, 36832, 73664, 73124, 146248, 292496, 584992, 584182, 1168364,
268364, 536728, 1073456, 2146912, 4293824, 8587648, 17175296, 34350592, 68701184,
6870284, 13740568, 27481136, 2748236, 5496472, 10992944, 1018298, 2036596, 4073192,
8146384, 16292768, 32585536, 32581036, 65162072, 130324144, 13032418, 26064836,
52129672, 104259344, 10425938, 20851876, 41703752, 83407504, 166815008, 11281508,
2281508, 481508, 963016, 1926032, 3852064, 7704128, 1404128, 2808256, 5616512, 11233024,
226024, 46024, 92048, 184096, 368192, 736384, 1472768, 2945536, 2941036, 5882072,
5162072, 10324144, 1032418, 2064836, 4129672, 8259344, 825938, 1651876, 3303752,
603752, 1207504, 2415008, 241508, 483016, 966032, 912032, 1824064, 3648128, 7296256,
14592512, 29185024, 58370048, 5837048, 11674096, 2674096, 5348192, 10696384, 21392768,
42785536, 42781036, 85562072, 81062072, 162124144, 16212418, 32424836, 64849672,
129699344, 12961838, 25923676, 51847352, 103694704, 207389408, 414778816, 414141616,
828283232, 1656566464, 1656512464, 3313024928, 613024928, 1226049856, 146049856,
292099712, 292018712, 584037424, 1168074848, 268074848, 536149696, 1072299392, 107418392,
214836784, 429673568, 859347136, 1718694272, 3437388544, 343731658, 687463316, 68746616,
68741216, 137482432, 274964864, 549929728, 541829728, 1083659456, 2167318912, 4334637824,
464637824, 929275648, 1858551296, 1858101296, 3716202592, 7432405184, 14864810368,
29729620736, 59459241472, 118918482944, 2891848298, 5783696596, 11567393192, 2567393192,
5134786384, 10269572768, 20539145536, 20539141036, 41078282072, 82156564144, 8215656418,
16431312836, 32862625672, 65725251344, 6572525138, 13145050276, 26290100552, 2629010102,
5258020204, 10516040408, 21032080816, 42064161632, 84128323264, 168256646528, 168251246528,
336502493056, 66502493056, 12502493056, 25004986112, 250498622, 25049864, 50099728,
5018728, 10037456, 1037456, 2074912, 4149824, 8299648, 8218648, 16437296, 32874592,
65749184, 131498368, 262996736, 262186736, 524373472, 1048746944, 104874698, 209749396,
419498792, 838997584, 838187584, 1676375168, 3352750336, 65275066, 65275012, 130550024,
13010024, 1301024, 2602048, 5204096, 10408192, 20816384, 41632768, 83265536, 83261036,
166522072, 11254072, 2254072, 454072, 908144, 90818, 181636, 363272, 726544, 72658,
145316, 290632, 581264, 1162528, 262528, 525056, 1050112, 105022, 10504, 21008,
2108, 4216, 8432, 16864, 33728, 6728, 13456, 26912, 53824, 107648, 215296, 430592,
861184, 86284, 172568, 345136, 690272, 1380544, 138058, 276116, 27626, 55252, 10252,
20504, 41008, 4108, 8216, 16432, 32864, 65728, 131456, 262912, 525824, 1051648,
2103296, 4206592, 8413184, 16826368, 33652736, 6652736, 1252736, 2505472, 5010944,
501098, 1002196, 102196, 204392, 408784, 817568, 1635136, 3270272, 6540544, 654058,
1308116, 130826, 261652, 523304, 52604, 105208, 210416, 420832, 841664, 841124,
84224, 8444, 812, 1624, 3248, 6496, 12992, 12182, 24364, 48728, 97456, 194912, 389824,
779648, 149648, 299296, 218296, 436592, 873184, 1746368, 3492736, 6985472, 13970944,
1397098, 2794196, 5588392, 1016392, 2032784, 4065568, 4061068, 8122136, 814136,
1628272, 3256544, 325658, 651316, 1302632, 2605264, 5210528, 10421056, 20842112,
2084222, 20846, 41692, 83384, 8684, 17368, 34736, 69472, 138944, 13898, 27796, 21496,
42992, 42182, 84364, 168728, 337456, 67456, 134912, 269824, 539648, 1079296, 2158592,
4317184, 8634368, 17268736, 34537472, 69074944, 6907498, 13814996, 13814186, 27628372,
55256744, 1025678, 2051356, 4102712, 8205424, 16410848, 32821696, 65643392, 6564692,
13129384, 26258768, 52517536, 105035072, 210070144, 2107018, 4214036, 8428072, 16856144,
1685618, 3371236, 671236, 1342472, 2684944, 268498, 536996, 536186, 1072372, 2144744,
21878, 43756, 87512, 175024, 350048, 35048, 70096, 7096, 14192, 28384, 56768, 113536,
23536, 47072, 94144, 9418, 18836, 11636, 2636, 5272, 10544, 1058, 2116, 226, 46,
92, 184, 368, 736, 1472, 2944, 298, 596, 1192, 292, 584, 1168, 268, 536, 1072, 2144, 218, 436, 872,
1744, 178, 356, 712, 1424, 2848, 5696, 11392, 2392, 4784, 9568, 19136, 38272, 76544,
7658, 15316, 30632, 61264, 122528, 14528, 29056, 58112, 5822, 584}
__________
Thanks to Allan, Hans and Jean-Marc for their neat job!
Best,
É.