A108399 Least positive k such that n^2 + k is a golden semiprime (A108540).

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

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

Cf. A108540.

Sequence in context: A292580 A301914 A180706 * A094772 A263832 A351952

Adjacent sequences: A108396 A108397 A108398 * A108400 A108401 A108402

Keyword

easy,nonn

Author

Jason Earls, Jul 03 2005

Status

approved