%I #6 Nov 28 2019 06:13:34
%S 3,5,11,17,31,37,47,59,67,109,127,157,163,167,173,211,241,263,271,293,
%T 313,367,389,439,449,457,503,571,593,613,619,643,661,677,701,727,739,
%U 787,823,911,983,991,1021,1069,1163,1187,1231,1289,1381,1429,1487,1523
%N Greater prime factor of n-th golden semiprime.
%C abs(phi*A108541(n) - a(n)) < 1, where phi = golden ratio = (1+sqrt(5))/2.
%H Amiram Eldar, <a href="/A108542/b108542.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A108540(n)/A108541(n).
%t 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 *)
%Y Cf. A001622, A084127, A108540, A108541, A108543, A108544.
%Y Subsequence of A108539.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 09 2005