%I #27 Dec 10 2014 02:03:04
%S 339887,458683,638117,628189,902449,418939,189391,386891,235369,
%T 693179,607667,595939,613199,171169,631361,497587,864449,987433,
%U 544877,647809,217057,705751,427621,410117,666599,979873,731761,874807,530567,228911
%N Primes from merging of 6 successive digits in decimal expansion of the Golden Ratio; (1+sqrt(5))/2.
%C Leading zeros are not permitted, so each term is 6 digits in length. - _Harvey P. Dale_, Oct 23 2011
%H Vincenzo Librandi, <a href="/A103808/b103808.txt">Table of n, a(n) for n = 1..1000</a>
%H Mohammad K. Azarian, <a href="http://www.math-cs.ucmo.edu/~mjms/1998.3/prob.ps">Problem 123</a>, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3, Fall 1998, p. 176. <a href="http://www.math-cs.ucmo.edu/~mjms/2000.1/soln.ps">Solution</a> published in Vol. 12, No. 1, Winter 2000, pp. 61-62.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRatio.html">The Golden Ratio</a>.
%H <a href="http://www.gutenberg.org/ebooks/634">Expansion of the Golden Ratio </a> to 20,000 digits as part of project Gutenberg.
%t With[{len=6},FromDigits/@Select[Partition[RealDigits[GoldenRatio,10, 1000][[1]],len,1],PrimeQ[FromDigits[#]] &&IntegerLength[ FromDigits[#]] ==len&]] (* _Harvey P. Dale_, Oct 23 2011 *)
%o (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
%Y Cf. A198177, A103773, A103789, A103793, A103808 (this), A103809, A103810, A103811, A103812; A103752.
%Y 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.
%K nonn,base
%O 1,1
%A Andrew G. West (WestA(AT)wlu.edu), Mar 29 2005
%E Offset changed from 0 to 1 by _Vincenzo Librandi_, Apr 22 2013