

A108539


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


10



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
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OFFSET

1,1


COMMENTS

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


LINKS

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


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 *)


CROSSREFS

Cf. A001622, A007067, A108540.
A108542 is a subsequence.
Sequence in context: A222176 A331891 A331896 * A170886 A238137 A090919
Adjacent sequences: A108536 A108537 A108538 * A108540 A108541 A108542


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Jun 09 2005


EXTENSIONS

Corrected by T. D. Noe, Oct 25 2006


STATUS

approved



