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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
OFFSET
1,1
COMMENTS
Leading zeros are not permitted, so each term is 6 digits in length. - Harvey P. Dale, Oct 23 2011
LINKS
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
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