|
|
A108399
|
|
Least positive k such that n^2 + k is a golden semiprime (A108540).
|
|
1
|
|
|
5, 2, 6, 61, 52, 41, 28, 13, 106, 87, 66, 43, 18, 393, 364, 333, 300, 265, 228, 189, 148, 105, 60, 13, 226, 175, 122, 67, 10, 463, 402, 339, 274, 207, 138, 67, 814, 739, 662, 583, 502, 419, 334, 247, 158, 67, 538, 443, 346, 247, 146, 43, 4494, 4387, 4278, 4167, 4054
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|