|
| |
|
|
A059791
|
|
Numbers n such that floor(phi^n) is prime, where phi = golden ratio.
|
|
3
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
