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

1,1

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

Formula

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

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 *)

Crossrefs

Cf. A001622, A084127, A108540, A108541, A108543, A108544.

Subsequence of A108539.

Sequence in context: A309437 A309438 A309439 * A006450 A085918 A267094

Adjacent sequences: A108539 A108540 A108541 * A108543 A108544 A108545

Keyword

nonn

Author

Reinhard Zumkeller, Jun 09 2005

Status

approved