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

2, 5, 7, 11, 13, 17, 19, 31, 37, 41, 47, 53, 61, 71, 79, 113, 313, 353, 503, 613, 617, 863, 1097, 1361, 4787, 4793, 5851, 7741, 8467, 10691, 12251, 13963, 14449, 19469, 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

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Nov 17 2009

Keywords

• nonn

Comments

Primes in A059791. - Charles R Greathouse IV, Jul 29 2011

Also primes in A001606. - Michel Marcus, Oct 21 2016

Crossrefs

Cf. A001606, A059791.

Programs

Magma

[p: p in PrimesUpTo(2000)| IsPrime(Lucas(p))]; // Vincenzo Librandi, Jul 11 2019

Mathematica

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

PARI

phi=(1+sqrt(5))/2;forprime(p=2,1e3,if(isprime(floor(phi^p)),print1(p", "))) \\ Charles R Greathouse IV, Jul 29 2011

Extensions

a(22)-a(32) from Charles R Greathouse IV, Jul 29 2011

More terms (using A001606) from Joerg Arndt, Jul 11 2019