A175593 Numbers k such that 2*k has no primitive root but 2*k-1 and 2*k+1 both have primitive roots.

4, 6, 12, 14, 15, 21, 24, 30, 36, 40, 51, 54, 63, 69, 75, 84, 90, 96, 99, 114, 120, 135, 141, 156, 174, 180, 210, 216, 231, 261, 285, 300, 309, 321, 330, 364, 405, 411, 414, 420, 429, 441, 510, 516, 525, 531, 546, 576, 615, 639, 645, 651, 660, 684, 714, 726, 741

Offset: 1

Author

Vladislav-Stepan Malakhovsky and Juri-Stepan Gerasimov, Jul 20 2010

Keywords

• nonn

Examples

			4 is in the sequence because 8 is not in A033948 but 7 and 9 are.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033948, A046145.

Programs

Mathematica

noprQ[n_] := ! IntegerQ @ PrimitiveRoot[n]; q[n_] := noprQ /@ (2*n + {-1, 0, 1}) == {False, True, False}; Select[Range[2, 1000], q] (* Amiram Eldar, Oct 03 2021 *)

Formula

{k: A046145(2*k)=0 and A046145(2*k-1)>0 and A046145(2*k+1)>0}.