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A108539 a(n) = that prime p such that p/prime(n) is nearest to phi, the golden ratio: phi=(1+sqrt(5))/2. 10

%I

%S 3,5,7,11,17,23,29,31,37,47,53,59,67,71,79,83,97,97,109,113,113,127,

%T 137,149,157,163,167,173,179,181,211,211,223,223,241,241,257,263,271,

%U 281,293,293,311,313,317,317,337,359,367,373,379,389,389,409,419,421,433

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

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

%H Amiram Eldar, <a href="/A108539/b108539.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>

%t 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 *)

%Y Cf. A001622, A007067, A108540.

%Y A108542 is a subsequence.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jun 09 2005

%E Corrected by _T. D. Noe_, Oct 25 2006

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Last modified June 22 14:22 EDT 2021. Contains 345380 sequences. (Running on oeis4.)