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

Author

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

Keywords

• nonn
• base

Comments

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

Links

• 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.

Crossrefs

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.

Programs

Mathematica

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

PARI

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

Extensions

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