

A198177


10digit primes found in the decimal expansion of the Golden Ratio phi, in the order of occurrence.


31



1772030917, 4189391137, 6222353693, 7931800607, 5959395829, 5829056383, 3832266131, 6131992829, 6892501711, 9250171169, 1043216269, 3136144381, 7587012203, 7954454749, 8509874339, 4487706647, 1240076521, 7780531531, 5315317141, 1704666599, 7046665991
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OFFSET

1,1


COMMENTS

Leading zeros are not permitted, so each term is 10 digits in length.
The sequence A103752 has erroneously the same definition; the actual definition of the terms is unknown.  M. F. Hasler, Nov 01 2014


LINKS

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


MATHEMATICA

With[{len=10}, Select[FromDigits/@Partition[RealDigits[GoldenRatio, 10, 1000][[1]], len, 1], IntegerLength[#]==len&&PrimeQ[#]&]]


PROG

(PARI) default(realprecision, N=1000); m=10^10; phi=sqrt(5/4)+.5; for(k=9, N, isprime(phi\.1^k%m)next; (p=phi\.1^k%m)>10^9&&print1(p", ")) \\ M. F. Hasler, Oct 31 2014


CROSSREFS

Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812; A103752.
See also, for e: A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851; for Pi: A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174; for sqrt(2): A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198161; for the EulerMascheroni constant gamma: A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784.
Sequence in context: A258423 A174762 A147769 * A129616 A105006 A090874
Adjacent sequences: A198174 A198175 A198176 * A198178 A198179 A198180


KEYWORD

nonn,base


AUTHOR

Harvey P. Dale, Oct 21 2011


STATUS

approved



