OFFSET
1,1
COMMENTS
Conjecture: for every n > 4 there exists a number k < n^[n/2] such that k*n + 1 is a golden semiprime, where [] is the floor function.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
EXAMPLE
a(3) = 62 because 62*3+1 = 187 = 11*17 and 11*phi-17 = 0.7983... < 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[k * n + 1], k++]; k]; Array[a, 54] (* Amiram Eldar, Nov 29 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jason Earls, Jun 15 2005
STATUS
approved