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%I #35 Feb 09 2021 01:55:14
%S 1,17,41,97,137,193,241,313,401,409,433,449,457,521,569,641,673,761,
%T 769,809,857,929,953,977,1009,1129,1297,1321,1361,1409,1489,1657,1697,
%U 1873,1993,2017,2081,2137,2153,2161
%N Numbers k such that (2*k-1)*(2^((k-1)/4)) == 1 (mod k).
%C It appears that many elements of this sequence are prime. The first "pseudoprime" in this sequence is 74665.
%H Charles R Greathouse IV, <a href="/A293394/b293394.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, 3001, 4], #==1 || Mod[-PowerMod[#-2, (#-1)/4, #], #]==1&] (* _Jean-François Alcover_, Nov 18 2018 *)
%o (PARI) is(n)=n%4==1 && (2*n-1)*Mod(2,n)^(n>>2)==1 \\ _Charles R Greathouse IV_, Nov 09 2017
%Y Cf. A001133, A244626, A294717.
%K nonn
%O 1,2
%A _Jonas Kaiser_, Nov 09 2017
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