[seqfan] Re: 1951-numbers

Tue Dec 22 09:20:14 CET 2015

Hello,

I find the first 1000 terms to be:
11, 16, 17, 27, 47, 52, 57, 78, 87, 117, 131, 151, 157, 158, 161, 171, 177, 187, 191, 247, 257, 277, 417, 447, 457, 487, 517, 547, 557, 558, 587, 592, 717, 747, 757, 787, 817, 857, 887, 1131, 1147, 1151, 1157, 1161, 1167, 1171, 1177, 1181, 1191, 1221, 1247, 1251, 1257, 1261, 1287, 1331, 1361, 1371, 1417, 1431, 1441, 1447, 1457, 1461, 1471, 1487, 1517, 1521, 1531, 1551, 1557, 1571, 1581, 1587, 1598, 1631, 1651, 1661, 1671, 1681, 1731, 1747, 1758, 1761, 1771, 1787, 1817, 1821, 1831, 1847, 1851, 1857, 1861, 1867, 1871, 1887, 1891, 1931, 1951, 1961, 1971, 1991, 2147, 2151, 2157, 2161, 2171, 2217, 2257, 2258, 2277, 2287, 2347, 2357, 2417, 2447, 2487, 2517, 2547, 2557, 2577, 2587, 2747, 2787, 2797, 2817, 2847, 2857, 2887, 3113, 3151, 3161, 3171, 3181, 3313, 3747, 3757, 4131, 4147, 4151, 4157, 4161, 4171, 4187, 4197, 4217, 4257, 4267, 4287, 4447, 4449, 4457, 4467, 4477, 4517, 4547, 4567, 4587, 4617, 4647, 4667, 4687, 4757, 4787, 4817, 4847, 4857, 4867, 4887, 4897, 4992, 5121, 5131, 5147, 5157, 5161, 5171, 5217, 5247, 5277, 5287, 5417, 5447, 5457, 5487, 5517, 5547, 5552, 5557, 5577, 5587, 5597, 5598, 5714, 5758, 5787, 5847, 5857, 5992, 5994, 6121, 6131, 6151, 6171, 6181, 6747, 6787, 6811, 7151, 7157, 7161, 7187, 7191, 7247, 7257, 7417, 7423, 7447, 7457, 7467, 7487, 7517, 7547, 7557, 7577, 7587, 7598, 7747, 7758, 7787, 7794, 7817, 7857, 7877, 7887, 7998, 8121, 8131, 8147, 8151, 8157, 8161, 8171, 8187, 8191, 8257, 8287, 8417, 8447, 8457, 8487, 8557, 8587, 8747, 8817, 8847, 8857, 8877, 8887, 8889, 9131, 9151, 9161, 9171, 9556, 9598, 9747, 9757, 9787, 9899, 9994, 11117, 11131, 11151, 11157, 11161, 11166, 11171, 11186, 11187, 11191, 11217, 11247, 11251, 11257, 11261, 11267, 11281, 11291, 11331, 11361, 11371, 11381, 11421, 11431, 11447, 11461, 11471, 11511, 11517, 11531, 11547, 11551, 11561, 11567, 11571, 11581, 11587, 11617, 11631, 11647, 11651, 11661, 11671, 11681, 11717, 11721, 11731, 11747, 11751, 11757, 11758, 11761, 11771, 11787, 11817, 11831, 11851, 11857, 11858, 11861, 11867, 11871, 11887, 11897, 11931, 11961, 11971, 11981, 11991, 12131, 12147, 12157, 12161, 12171, 12177, 12181, 12191, 12217, 12247, 12251, 12281, 12287, 12361, 12371, 12417, 12447, 12461, 12471, 12487, 12517, 12531, 12547, 12551, 12557, 12571, 12581, 12587, 12597, 12631, 12651, 12661, 12671, 12751, 12757, 12761, 12771, 12787, 12831, 12847, 12851, 12857, 12861, 12871, 12881, 12931, 12951, 12961, 12971, 13131, 13151, 13161, 13171, 13181, 13191, 13251, 13261, 13331, 13361, 13371, 13381, 13431, 13449, 13461, 13471, 13531, 13543, 13547, 13551, 13557, 13561, 13571, 13577, 13611, 13631, 13661, 13671, 13751, 13761, 13771, 13831, 13851, 13871, 13931, 13951, 13961, 13971, 13981, 14121, 14131, 14151, 14157, 14161, 14171, 14191, 14251, 14257, 14261, 14331, 14361, 14381, 14417, 14421, 14431, 14443, 14447, 14457, 14461, 14471, 14487, 14517, 14531, 14547, 14557, 14561, 14571, 14591, 14631, 14651, 14661, 14671, 14681, 14691, 14731, 14747, 14751, 14758, 14761, 14771, 14787, 14817, 14831, 14851, 14857, 14871, 14881, 14887, 14931, 14951, 14961, 14971, 15131, 15147, 15157, 15161, 15171, 15181, 15191, 15217, 15247, 15251, 15261, 15277, 15281, 15331, 15361, 15371, 15417, 15431, 15447, 15457, 15461, 15471, 15487, 15517, 15551, 15553, 15556, 15557, 15561, 15571, 15581, 15587, 15598, 15631, 15651, 15661, 15671, 15747, 15751, 15758, 15761, 15771, 15787, 15817, 15831, 15847, 15851, 15857, 15858, 15861, 15871, 15881, 15887, 15898, 15931, 15951, 15961, 15971, 15998, 16131, 16151, 16161, 16171, 16181, 16191, 16251, 16261, 16276, 16331, 16361, 16371, 16431, 16451, 16461, 16471, 16531, 16547, 16551, 16557, 16571, 16587, 16631, 16661, 16671, 16681, 16731, 16751, 16761, 16771, 16781, 16831, 16851, 16861, 16871, 16931, 16951, 16961, 16971, 16981, 17121, 17141, 17147, 17151, 17161, 17171, 17191, 17217, 17247, 17251, 17257, 17261, 17267, 17361, 17417, 17421, 17447, 17457, 17461, 17471, 17497, 17517, 17547, 17551, 17557, 17571, 17587, 17631, 17651, 17661, 17671, 17681, 17719, 17721, 17731, 17741, 17747, 17751, 17757, 17758, 17761, 17771, 17777, 17817, 17831, 17847, 17851, 17861, 17871, 17881, 17931, 17951, 17961, 17971, 17991, 18131, 18147, 18157, 18161, 18171, 18187, 18191, 18197, 18247, 18251, 18257, 18258, 18261, 18267, 18281, 18287, 18331, 18371, 18431, 18447, 18457, 18461, 18467, 18471, 18517, 18531, 18551, 18558, 18561, 18571, 18581, 18587, 18617, 18647, 18651, 18661, 18667, 18671, 18687, 18747, 18761, 18771, 18781, 18787, 18817, 18831, 18851, 18857, 18871, 18887, 18897, 18931, 18951, 18961, 18971, 19131, 19151, 19161, 19181, 19191, 19221, 19251, 19261, 19291, 19331, 19361, 19371, 19431, 19461, 19471, 19521, 19531, 19547, 19551, 19557, 19571, 19587, 19597, 19631, 19651, 19661, 19671, 19681, 19711, 19731, 19751, 19761, 19771, 19821, 19831, 19851, 19861, 19871, 19911, 19931, 19951, 19961, 19971, 21131, 21151, 21157, 21161, 21171, 21181, 21211, 21247, 21251, 21257, 21261, 21281, 21317, 21347, 21361, 21387, 21417, 21431, 21447, 21451, 21457, 21461, 21467, 21471, 21487, 21521, 21547, 21551, 21557, 21571, 21587, 21651, 21661, 21671, 21747, 21751, 21758, 21761, 21771, 21787, 21817, 21821, 21831, 21851, 21857, 21871, 21881, 21887, 21951, 21961, 22131, 22147, 22157, 22167, 22171, 22177, 22181, 22187, 22211, 22217, 22247, 22257, 22258, 22287, 22317, 22347, 22357, 22387, 22397, 22417, 22447, 22487, 22517, 22557, 22587, 22588, 22747, 22758, 22787, 22817, 22828, 22867, 22887, 23131, 23147, 23151, 23157, 23171, 23217, 23257, 23277, 23347, 23357, 23377, 23417, 23447, 23487, 23517, 23557, 23567, 23587, 23717, 23747, 23773, 23787, 23797, 23847, 23857, 23887, 24147, 24151, 24161, 24171, 24181, 24217, 24247, 24257, 24267, 24277, 24287, 24317, 24347, 24357, 24387, 24417, 24447, 24457, 24487, 24497, 24517, 24547, 24557, 24587, 24747, 24817, 24847, 24887, 25117, 25121, 25147, 25151, 25157, 25161, 25171, 25197, 25217, 25257, 25267, 25287, 25317, 25357, 25367, 25377, 25447, 25457, 25467, 25512, 25547, 25587, 25617, 25647, 25677, 25687, 25747, 25757, 25758, 25787, 25817, 25838, 25847, 25857, 25867, 25887, 25897, 25992, 26151, 26161, 26171, 26347, 26357, 26387, 26669, 26889, 27121, 27147, 27151, 27157, 27161, 27171, 27187, 27191, 27247, 27257, 27277, 27287, 27347, 27357, 27397, 27417, 27457, 27487, 27497, 27547, 27557, 27577, 27597, 27747, 27757, 27787, 27817, 27847, 27857, 27897, 27917, 27947, 27957, 27987, 27997, 28121, 28131, 28151, 28157, 28161, 28171, 28181, 28187, 28191, 28238, 28257, 28417, 28447, 28457, 28487, 28517, 28587, 28747, 28787, 28811, 28817, 28857, 28887, 29151, 29161, 29171, 31121, 31131, 31138, 31151, 31161, 31171, 31181, 31251, 31261, 31331, 31358, 31361, 31371, 31381, 31421, 31461, 31471, 31531, 31551, 31561, 31571, 31631, 31661

/Lars B

-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Eric Angelini
Skickat: den 14 december 2015 16:40
Till: Sequence Fanatics <seqfan at list.seqfan.eu>
Kopia: alexandre.wajnberg at skynet.be
Ämne: [seqfan] 1951-numbers

Hello SeqFans,

If you insert a "division symbol" anywhere between two digits of 1951, you will produce a fraction F whose decimal expansion will show the different digits present in F:

1951:

F = 1/951 = 0.001051524710830704521556256572029443...
F = 19/51 = 0.37254901960784...
F = 195/1 = 195

I guess the seq S of integers sharing this property starts:
S = 11, 16, ...

(no integer part of S will show a zero at some place, of course) Best, É.

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