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 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 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

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Last modified August 10 22:36 EDT 2022. Contains 356046 sequences. (Running on oeis4.)