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

1,1

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

Formula

a(n) = A108540(n)/A108542(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]; If[f[p] > 0, AppendTo[seq, p]], {200}]; seq (* Amiram Eldar, Nov 28 2019 *)

Crossrefs

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

Sequence in context: A090666 A140409 A201011 * A038937 A092940 A045326

Adjacent sequences: A108538 A108539 A108540 * A108542 A108543 A108544

Keyword

nonn

Author

Reinhard Zumkeller, Jun 09 2005

Status

approved