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A198177 10-digit 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 (list; graph; refs; listen; history; text; internal format)



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


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


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


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 A090874

Adjacent sequences:  A198174 A198175 A198176 * A198178 A198179 A198180




Harvey P. Dale, Oct 21 2011



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Last modified November 21 17:44 EST 2017. Contains 295004 sequences.