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

1,1

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

Formula

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

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

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 *)

Crossrefs

Cf. A108539, A165569, A165570, A165572.

Sequence in context: A273006 A352538 A117763 * A178954 A138111 A218100

Adjacent sequences: A165568 A165569 A165570 * A165572 A165573 A165574

Keyword

nonn

Author

Antti Karttunen, Sep 22 2009

Extensions

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

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

Status

approved