A165571 Lesser prime factor of successively better golden semiprimes.

2, 3, 7, 19, 23, 29, 97, 353, 563, 631, 919, 1453, 2207, 15271, 15737, 42797, 49939, 133559, 179317, 287557, 508451, 918011, 1103483, 1981891, 9181097, 16958611, 17351447, 52204391, 66602803, 99641617, 134887397, 487195147, 629449511, 943818943, 1527963169, 2048029369

Offset: 1

Author

Antti Karttunen, Sep 22 2009

Keywords

• nonn

Comments

See A165569 and A165570 for the definition. Probably a subset of A108541.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..48

Crossrefs

Cf. A108539, A165569, A165570, A165572.

Programs

Mathematica

f[p_] := Module[{x = GoldenRatio * p, p1, p2}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; If[p2 - x > x - p1, p1, p2]]; seq={}; dm = 1; p1 = 1; Do[p1 = NextPrime[p1]; k++; p2 = f[p1]; d = Abs[p2/p1 - GoldenRatio]; If[d < dm, dm = d; AppendTo[seq, p1]], {10^4}]; seq  (* Amiram Eldar, Nov 28 2019 *)

Formula

a(n) = A000040(A165569(n)).

a(n) = A165570(n)/A165572(n).

Extensions

a(16)-a(23) from Donovan Johnson, May 13 2010

a(24)-a(36) from Amiram Eldar, Nov 28 2019