A059791 Numbers n such that floor(phi^n) is prime, where phi = golden ratio.

2, 5, 6, 7, 11, 13, 17, 19, 24, 31, 37, 41, 47, 48, 53, 61, 71, 79, 96, 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

Offset

1,1

Comments

Tested up to n=250000. - Mark Rodenkirch, Feb 27 2020

Links

Table of n, a(n) for n=1..52.

Eric Weisstein's World of Mathematics, Phi-Prime

Example

floor(phi^863)=227160876495918562748535035942584201965901433059749617\
427535706949917136103176482875403653972639455945062095866005032008819\
9236184776437699830957031191632116265394965429613743580479 is prime.

Mathematica

Block[{$MaxExtraPrecision=10000}, Select[Range[14000], PrimeQ[ Floor[ GoldenRatio^#]]&]] (* Harvey P. Dale, Mar 06 2017 *)

Prog

(PARI) isok(n) = isprime(floor(((sqrt(5)+1)/2)^n)) \\ Michel Marcus, Jul 14 2013
Terms generated and tested with pfgw then verified with PARI using the following:
(PARI) c(n) = 3*fibonacci(n-1) + fibonacci(n-2) + (n % 2) - 1; ispseudoprime(c(n)) \\ Mark Rodenkirch, Feb 27 2020

Crossrefs

Cf. A001622, A059792.

Sequence in context: A344170 A292115 A283476 * A043329 A023699 A058605

Adjacent sequences: A059788 A059789 A059790 * A059792 A059793 A059794

Keyword

nonn

Author

Naohiro Nomoto, Feb 22 2001

Extensions

More terms from Vladeta Jovovic, Feb 24 2001

a(27)-a(33) from Eric W. Weisstein, May 01 2006

a(34)-a(36) from Dmitry Kamenetsky, Dec 29 2008

a(37)-a(52) from Mark Rodenkirch, Feb 27 2020

Status

approved