A108200 Least positive k such that k*n + 1 is a golden semiprime (A108540).

5, 7, 62, 19, 1, 31, 2, 1254, 1692, 85, 912, 49, 20796, 1, 1234, 627, 50, 846, 4, 860, 28, 456, 4076, 418, 34, 10398, 564, 21, 91250, 617, 6, 47670, 304, 25, 6218, 423, 352018, 2, 6932, 430, 9348, 14, 400, 228, 2874, 2038, 324, 209, 12, 17, 5562, 5199, 25784, 282

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

Cf. A108540.

Sequence in context: A268433 A201109 A177336 * A077780 A307361 A260829

Adjacent sequences: A108197 A108198 A108199 * A108201 A108202 A108203

Keyword

nonn

Author

Jason Earls, Jun 15 2005

Status

approved