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

1,1

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A033948, A046145.

Sequence in context: A359040 A310595 A350864 * A163097 A110178 A318712

Adjacent sequences: A175590 A175591 A175592 * A175594 A175595 A175596

Keyword

nonn

Author

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

Status

approved