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A168033 Primes p such that floor(phi^p) is prime. 2

%I #22 Sep 08 2022 08:45:48

%S 2,5,7,11,13,17,19,31,37,41,47,53,61,71,79,113,313,353,503,613,617,

%T 863,1097,1361,4787,4793,5851,7741,8467,10691,12251,13963,14449,19469,

%U 35449,36779,44507,51169,56003,81671,89849,94823,140057,148091,159521,183089,193201,202667,344293,387433,443609,532277,574219,616787,631181,637751,651821,692147,901657,1051849

%N Primes p such that floor(phi^p) is prime.

%C Primes in A059791. - _Charles R Greathouse IV_, Jul 29 2011

%C Also primes in A001606. - _Michel Marcus_, Oct 21 2016

%t $MaxExtraPrecision=6!; Select[Prime[Range[5! ]],PrimeQ[Floor[GoldenRatio^# ]]&]

%o (PARI) phi=(1+sqrt(5))/2;forprime(p=2,1e3,if(isprime(floor(phi^p)),print1(p", "))) \\ _Charles R Greathouse IV_, Jul 29 2011

%o (Magma) [p: p in PrimesUpTo(2000)| IsPrime(Lucas(p))]; // _Vincenzo Librandi_, Jul 11 2019

%Y Cf. A001606, A059791.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Nov 17 2009

%E a(22)-a(32) from _Charles R Greathouse IV_, Jul 29 2011

%E More terms (using A001606) from _Joerg Arndt_, Jul 11 2019

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)