%I

%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 n such that 2^((n-1)/3) = 1 mod n and (2*n-1)*(2^((n-1)/6)) = 1 mod n.

%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.

%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,new

%O 1,2

%A _Jonas Kaiser_, Nov 07 2017