A198177 10-digit primes found in the decimal expansion of the Golden Ratio phi, in the order of occurrence.

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

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 Euler-Mascheroni constant gamma: A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784.

Sequence in context: A258423 A174762 A147769 * A129616 A105006 A318788

Adjacent sequences: A198174 A198175 A198176 * A198178 A198179 A198180

Keyword

nonn,base

Author

Harvey P. Dale, Oct 21 2011

Status

approved