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

Author

Harvey P. Dale, Oct 21 2011

Keywords

• nonn
• base

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

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.

Programs

Mathematica

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

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