A108542 Greater prime factor of n-th golden semiprime.

3, 5, 11, 17, 31, 37, 47, 59, 67, 109, 127, 157, 163, 167, 173, 211, 241, 263, 271, 293, 313, 367, 389, 439, 449, 457, 503, 571, 593, 613, 619, 643, 661, 677, 701, 727, 739, 787, 823, 911, 983, 991, 1021, 1069, 1163, 1187, 1231, 1289, 1381, 1429, 1487, 1523

Offset: 1

Author

Reinhard Zumkeller, Jun 09 2005

Keywords

• nonn

Comments

abs(phi*A108541(n) - a(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, A084127, A108540, A108541, A108543, A108544.

Subsequence of A108539.

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]; q = f[p]; If[q > 0, AppendTo[seq, q]], {200}]; seq (* Amiram Eldar, Nov 28 2019 *)

Formula

a(n) = A108540(n)/A108541(n).