A165572 Greater prime factor of successively better golden semiprimes.

3, 5, 11, 31, 37, 47, 157, 571, 911, 1021, 1487, 2351, 3571, 24709, 25463, 69247, 80803, 216103, 290141, 465277, 822691, 1485373, 1785473, 3206767, 14855327, 27439609, 28075231, 84468479, 107765599, 161223523, 218252393, 788298307, 1018470703, 1527131129, 2472296341

Offset

1,1

Comments

See A165569 and A165570 for the definition. Probably a subset of A108542.

Links

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

Formula

a(n) = A108539(A165569(n)).

a(n) = A165570(n)/A165571(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, p2]], {10^4}]; seq  (* Amiram Eldar, Nov 28 2019 *)

Crossrefs

Cf. A108539, A165569, A165570, A165571.

Sequence in context: A214089 A108259 A093933 * A246901 A236568 A095184

Adjacent sequences: A165569 A165570 A165571 * A165573 A165574 A165575

Keyword

nonn,more

Author

Antti Karttunen, Sep 22 2009

Extensions

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

a(24)-a(35) from Amiram Eldar, Nov 28 2019

Status

approved