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A171969 Smallest prime greater than phi^n. 1

%I

%S 2,3,5,7,13,19,31,47,79,127,211,331,523,853,1367,2207,3581,5779,9371,

%T 15131,24481,39607,64081,103687,167771,271451,439217,710663,1149857,

%U 1860503,3010363,4870861,7881221,12752053,20633279

%N Smallest prime greater than phi^n.

%H Charles R Greathouse IV, <a href="/A171969/b171969.txt">Table of n, a(n) for n = 1..4784</a>

%H M. Berg, <a href="http://www.fq.math.ca/Scanned/4-2/berg.pdf">Phi, the golden ratio (to 4599 decimal places) and Fibonacci numbers</a>, Fibonacci Quarterly, 4 (1966), 157-162.

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

%t 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}]

%t NextPrime[GoldenRatio^Range[40]] (* _Harvey P. Dale_, Dec 06 2013 *)

%o (PARI) a(n)=nextprime(((1+sqrt(5))/2)^n) \\ _Charles R Greathouse IV_, Jul 29 2011

%Y Cf. A001622, A104457.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 19 2010

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)