OFFSET
1,1
COMMENTS
Conjecture: for every n > 1 there exists a number k < n^3 such that n^2 + k is a golden semiprime.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
a(4)=61 because 4^2+61 = 77 = 7*11 and 7*phi-11 = 0.326237... < 1.
MATHEMATICA
goldQ[n_] := Module[{f = FactorInteger[n]}, If[Length[f] != 2, False, If[Max[f[[;; , 2]]] != 1, False, Abs[f[[2, 1]] - f[[1, 1]] * GoldenRatio] < 1]]]; a[n_] := Module[{k = 1}, While[!goldQ[n^2 + k], k++]; k]; Array[a, 57] (* Amiram Eldar, Nov 29 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jul 03 2005
STATUS
approved