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A198177 10-digit primes found in the decimal expansion of the Golden Ratio phi, in the order of occurrence. 31


%S 1772030917,4189391137,6222353693,7931800607,5959395829,5829056383,

%T 3832266131,6131992829,6892501711,9250171169,1043216269,3136144381,

%U 7587012203,7954454749,8509874339,4487706647,1240076521,7780531531,5315317141,1704666599,7046665991

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

%C Leading zeros are not permitted, so each term is 10 digits in length.

%C The sequence A103752 has erroneously the same definition; the actual definition of the terms is unknown. - _M. F. Hasler_, Nov 01 2014

%H Vincenzo Librandi, <a href="/A198177/b198177.txt">Table of n, a(n) for n = 1..1000</a>

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

%o (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

%Y Cf. A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812; A103752.

%Y 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.

%K nonn,base

%O 1,1

%A _Harvey P. Dale_, Oct 21 2011

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Last modified April 15 01:24 EDT 2021. Contains 342974 sequences. (Running on oeis4.)