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A103808 Primes from merging of 6 successive digits in decimal expansion of the Golden Ratio; (1+sqrt(5))/2. 30
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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 *)

PROG

(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

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.

Sequence in context: A234726 A132660 A236609 * A251996 A182132 A182515

Adjacent sequences:  A103805 A103806 A103807 * A103809 A103810 A103811

KEYWORD

nonn,base

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)