A108200 - OEIS

%I #7 Nov 29 2019 04:01:51

%S 5,7,62,19,1,31,2,1254,1692,85,912,49,20796,1,1234,627,50,846,4,860,

%T 28,456,4076,418,34,10398,564,21,91250,617,6,47670,304,25,6218,423,

%U 352018,2,6932,430,9348,14,400,228,2874,2038,324,209,12,17,5562,5199,25784,282

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

%C 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.

%H Amiram Eldar, <a href="/A108200/b108200.txt">Table of n, a(n) for n = 1..1000</a>

%e a(3) = 62 because 62*3+1 = 187 = 11*17 and 11*phi-17 = 0.7983... < 1.

%t 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 *)

%Y Cf. A108540.

%K nonn

%O 1,1

%A _Jason Earls_, Jun 15 2005