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%I #14 Oct 03 2021 04:52:04
%S 4,6,12,14,15,21,24,30,36,40,51,54,63,69,75,84,90,96,99,114,120,135,
%T 141,156,174,180,210,216,231,261,285,300,309,321,330,364,405,411,414,
%U 420,429,441,510,516,525,531,546,576,615,639,645,651,660,684,714,726,741
%N Numbers k such that 2*k has no primitive root but 2*k-1 and 2*k+1 both have primitive roots.
%H Amiram Eldar, <a href="/A175593/b175593.txt">Table of n, a(n) for n = 1..10000</a>
%F {k: A046145(2*k)=0 and A046145(2*k-1)>0 and A046145(2*k+1)>0}.
%e 4 is in the sequence because 8 is not in A033948 but 7 and 9 are.
%t 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 *)
%Y Cf. A033948, A046145.
%K nonn
%O 1,1
%A Vladislav-Stepan Malakhovsky and _Juri-Stepan Gerasimov_, Jul 20 2010
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