A108539 a(n) = that prime p such that p/prime(n) is nearest to phi, the golden ratio: phi=(1+sqrt(5))/2.

3, 5, 7, 11, 17, 23, 29, 31, 37, 47, 53, 59, 67, 71, 79, 83, 97, 97, 109, 113, 113, 127, 137, 149, 157, 163, 167, 173, 179, 181, 211, 211, 223, 223, 241, 241, 257, 263, 271, 281, 293, 293, 311, 313, 317, 317, 337, 359, 367, 373, 379, 389, 389, 409, 419, 421, 433

Offset: 1

Author

Reinhard Zumkeller, Jun 09 2005

Keywords

• nonn

Comments

a(n)*prime(n) is a term of A108540 iff abs(phi-a(n)/prime(n))<1.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Golden Ratio

Crossrefs

Cf. A001622, A007067, A108540.

A108542 is a subsequence.

Programs

Mathematica

a[n_] := Module[{x = GoldenRatio * Prime[n]}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; If[x - p1 < p2 - x, p1, p2]]; Array[a, 57] (* Amiram Eldar, Nov 28 2019 *)

Extensions

Corrected by T. D. Noe, Oct 25 2006