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%I #11 Nov 12 2023 00:06:15
%S 2047,4681,15841,42799,52633,90751,220729,256999,271951,486737,514447,
%T 647089,741751,916327,1082401,1145257,1730977,1969417,2205967,2304167,
%U 2748023,2811271,2953711,2976487,3567481,4188889,4469471,4835209,4863127,5016191,5049001,5681809
%N Base-2 Fermat pseudoprimes k such that the multiplicative order of 2 modulo k is odd.
%C The corresponding sequence for primes is A014663.
%C These pseudoprimes seem to be relatively rare: among the 118968378 base-2 Fermat pseudoprimes below 2^64 only 6292535 are terms of this sequence.
%C These pseudoprimes appear in a theorem by Rotkiewicz and Makowski (1966) about pseudoprimes that are products of two Mersenne numbers (see A367229).
%H Amiram Eldar, <a href="/A367230/b367230.txt">Table of n, a(n) for n = 1..10000</a>
%H Andrzej Rotkiewicz and Andrzej Makowski, <a href="https://doi.org/10.5169/seals-24655">On Pseudoprime Numbers of the Form M_p M_t</a>, Elemente der Mathematik, Vol. 21 (1966), pp. 133-134.
%t Select[2*Range[10^6] + 1, PowerMod[2, # - 1, #] == 1 && CompositeQ[#] && OddQ[MultiplicativeOrder[2, #]] &]
%o (PARI) is(n) = n > 1 && n % 2 && Mod(2, n)^(n-1) == 1 && !isprime(n) && znorder(Mod(2, n)) % 2;
%Y Intersection of A001567 and A036259.
%Y A367231 is a subsequence.
%Y Cf. A002326, A014663, A306413, A367229.
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 11 2023