A171969 Smallest prime greater than phi^n.

2, 3, 5, 7, 13, 19, 31, 47, 79, 127, 211, 331, 523, 853, 1367, 2207, 3581, 5779, 9371, 15131, 24481, 39607, 64081, 103687, 167771, 271451, 439217, 710663, 1149857, 1860503, 3010363, 4870861, 7881221, 12752053, 20633279

Offset: 1

Author

Michel Lagneau, Nov 19 2010

Keywords

• nonn

Examples

			The first prime > phi^6 = 17.94427... is 19, so a(6) = 19.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..4784
• M. Berg, Phi, the golden ratio (to 4599 decimal places) and Fibonacci numbers, Fibonacci Quarterly, 4 (1966), 157-162.

Crossrefs

Cf. A001622, A104457.

Programs

Mathematica

p[n_] := Module[{r, i}, r = 2; i = 1; While[r <= n, i = i + 1; r = Prime[i]];  r]; Table[p[GoldenRatio^n], {n, 1, 35}]
NextPrime[GoldenRatio^Range[40]] (* Harvey P. Dale, Dec 06 2013 *)

PARI

a(n)=nextprime(((1+sqrt(5))/2)^n) \\ Charles R Greathouse IV, Jul 29 2011