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%I #28 Feb 27 2020 15:14:40
%S 2,5,6,7,11,13,17,19,24,31,37,41,47,48,53,61,71,79,96,113,313,353,503,
%T 613,617,863,1097,1361,4787,4793,5851,7741,8467,10691,12251,13963,
%U 14449,19469,35449,36779,44507,51169,56003,81671,89849,94823,140057,148091,159521,183089,193201,202667
%N Numbers n such that floor(phi^n) is prime, where phi = golden ratio.
%C Tested up to n=250000. - _Mark Rodenkirch_, Feb 27 2020
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Phi-Prime.html">Phi-Prime</a>
%e floor(phi^863)=227160876495918562748535035942584201965901433059749617\
%e 427535706949917136103176482875403653972639455945062095866005032008819\
%e 9236184776437699830957031191632116265394965429613743580479 is prime.
%t Block[{$MaxExtraPrecision=10000}, Select[Range[14000],PrimeQ[ Floor[ GoldenRatio^#]]&]] (* _Harvey P. Dale_, Mar 06 2017 *)
%o (PARI) isok(n) = isprime(floor(((sqrt(5)+1)/2)^n)) \\ _Michel Marcus_, Jul 14 2013
%o Terms generated and tested with pfgw then verified with PARI using the following:
%o (PARI) c(n) = 3*fibonacci(n-1) + fibonacci(n-2) + (n % 2) - 1; ispseudoprime(c(n)) \\ _Mark Rodenkirch_, Feb 27 2020
%Y Cf. A001622, A059792.
%K nonn
%O 1,1
%A _Naohiro Nomoto_, Feb 22 2001
%E More terms from _Vladeta Jovovic_, Feb 24 2001
%E a(27)-a(33) from _Eric W. Weisstein_, May 01 2006
%E a(34)-a(36) from _Dmitry Kamenetsky_, Dec 29 2008
%E a(37)-a(52) from _Mark Rodenkirch_, Feb 27 2020
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