A108541 Lesser prime factor of n-th golden semiprime.

2, 3, 7, 11, 19, 23, 29, 37, 41, 67, 79, 97, 101, 103, 107, 131, 149, 163, 167, 181, 193, 227, 241, 271, 277, 283, 311, 353, 367, 379, 383, 397, 409, 419, 433, 449, 457, 487, 509, 563, 607, 613, 631, 661, 719, 733, 761, 797, 853, 883, 919, 941, 971, 997, 1031

Offset: 1

Author

Reinhard Zumkeller, Jun 09 2005

Keywords

• nonn

Comments

abs(phi*a(n) - A108542(n)) < 1, where phi = golden ratio = (1+sqrt(5))/2.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001622, A084126, A108539, A108540, A108542, A108543, A108544.

Programs

Mathematica

f[p_] := Module[{x = GoldenRatio * p}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; q = If[x - p1 < p2 - x, p1, p2]; If[Abs[q - x] < 1, q, 0]]; seq = {}; p=1; Do[p = NextPrime[p]; If[f[p] > 0, AppendTo[seq, p]], {200}]; seq (* Amiram Eldar, Nov 28 2019 *)

Formula

a(n) = A108540(n)/A108542(n).