A104944 -id:A104944 - cp's OEIS frontend

A103808 Primes from merging of 6 successive digits in decimal expansion of the Golden Ratio; (1+sqrt(5))/2.

339887, 458683, 638117, 628189, 902449, 418939, 189391, 386891, 235369, 693179, 607667, 595939, 613199, 171169, 631361, 497587, 864449, 987433, 544877, 647809, 217057, 705751, 427621, 410117, 666599, 979873, 731761, 874807, 530567, 228911

Offset: 1

Andrew G. West (WestA(AT)wlu.edu), Mar 29 2005

Leading zeros are not permitted, so each term is 6 digits in length. - Harvey P. Dale, Oct 23 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Mohammad K. Azarian, Problem 123, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3, Fall 1998, p. 176. Solution published in Vol. 12, No. 1, Winter 2000, pp. 61-62.
Eric Weisstein's World of Mathematics, The Golden Ratio.
Expansion of the Golden Ratio to 20,000 digits as part of project Gutenberg.

Cf. A198177, A103773, A103789, A103793, A103808 (this), A103809, A103810, A103811, A103812; A103752.

See also, for e: A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851; for Pi: A104824, A104825, A104826, A198170, A198171, A198172, A198173, A198175; for sqrt(2): A198161, A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169; for the Euler-Mascheroni constant gamma: A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784 and A104944.

With[{len=6},FromDigits/@Select[Partition[RealDigits[GoldenRatio,10, 1000][[1]],len,1],PrimeQ[FromDigits[#]] &&IntegerLength[ FromDigits[#]] ==len&]] (* Harvey P. Dale, Oct 23 2011 *)

A103808(n,x=(sqrt(5)+1)/2, m=6,silent=0)={m=10^m; for(k=1, default(realprecision), (isprime(p=x\.1^k%m)&&p*10>m)||next;silent||print1(p", ");n--||return(p))} \\ The optional arguments can be used to produce other sequences of this series (cf. Crossrefs). Use, e.g., \p999 to set precision to 999 digits. - M. F. Hasler, Nov 01 2014

Offset changed from 0 to 1 by Vincenzo Librandi, Apr 22 2013

A198784 Primes from merging of 10 successive digits in decimal expansion of Euler-Mascheroni constant (in the order of appearance).

Original entry on oeis.org

7215664901, 1566490153, 3286060651, 6060651209, 9008240243, 4310421593, 2159335939, 9235988057, 8486772677, 8070824809, 2836224173, 3622417399, 3997644923, 33374293, 2582470949, 6008735203, 87352039, 3151776611, 5015079847, 7400299213, 3139925401, 3754139549

Offset: 1

Harvey P. Dale, Oct 29 2011

Leading zeros are permitted, so some terms are less than 10 digits in length.

See A104944 for the variant where no leading zeros are allowed. - M. F. Hasler, Nov 01 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

For the Euler-Mascheroni constant, see also A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784 (this sequence) and A104944 (a variant).
For sqrt(2), see A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198161.
For e, see A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851.
For Pi, see A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174.
For the Golden Ratio, see A198177, A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812.

egp[len_]:=Module[{egterms=FromDigits/@Partition[RealDigits[EulerGamma, 10, 1000][[1]],len,1]},Select[egterms,PrimeQ[#]&]]; egp[10]

list_A198784(x=Euler,m=10)=m=10^m;for(k=1,default(realprecision),isprime(p=x\.1^k%m)&&print1(p",")) \\ The optional arguments can be used to produce other sequences of this series (cf. Crossrefs). Use e.g. \p999 to set precision to 999 digits. - M. F. Hasler, Nov 01 2014

cp's OEIS Frontend

A103808 Primes from merging of 6 successive digits in decimal expansion of the Golden Ratio; (1+sqrt(5))/2.

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