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%I #36 Feb 09 2021 01:55:17
%S 1,43,109,157,229,277,283,307,397,499,643,691,733,739,811,997,1021,
%T 1051,1069,1093,1459,1579,1597,1627,1699,1723,1789,1933,2179,2203,
%U 2251,2341,2347,2731,2749,2917,2971,3061,3163,3181,3229,3259,3277,3331,3373,3541,4027
%N Numbers k such that 2^((k-1)/3) == 1 (mod k) and (2*k-1)*(2^((k-1)/6)) == 1 (mod k).
%C Most of the elements of this sequence are prime. The "pseudoprimes" of these sequence are part of A244626.
%H Charles R Greathouse IV, <a href="/A294717/b294717.txt">Table of n, a(n) for n = 1..10000</a>
%H Jonas Kaiser, <a href="https://arxiv.org/abs/1608.00862">On the relationship between the Collatz conjecture and Mersenne prime numbers</a>, arXiv:1608.00862 [math.GM], 2016.
%t Select[Range[1, 6001, 6], # == 1 || PowerMod[2, (#-1)/3, #] == 1 && Mod[-PowerMod[2, (#-1)/6, #], #] == 1&] (* _Jean-François Alcover_, Nov 18 2018 *)
%o (PARI) is(n)=n%6==1 && Mod(2,n)^(n\3)==1 && (2*n-1)*Mod(2,n)^(n\6)==1 \\ _Charles R Greathouse IV_, Nov 08 2017
%Y Cf. A001133, A244626.
%K nonn
%O 1,2
%A _Jonas Kaiser_, Nov 07 2017
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