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A141629 a(n) is the least base-2 overpseudoprime k such that the multiplicative order of 2 mod k equals 8*n+20.

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%I A141629 #13 Nov 10 2023 09:23:58
%S A141629 3277,4033,838861,8321,80581,130561,104653,20647621,280601,818201,
%T A141629 68719214593,57646075230342349,48448661,1353244757701,351479006145541,
%U A141629 88357,390937,1846171781,17585969,9774181,28147501026509,3882413703281,1251949,9007199388958721
%N A141629 a(n) is the least base-2 overpseudoprime k such that the multiplicative order of 2 mod k equals 8*n+20.
%C A141629 C. Pomerance proved (private correspondence) that for every n>=1 there exists at least one overpseudoprime (a(n)) for which the multiplicative order of 2 mod a(n) equals 8n+20.
%C A141629 a(25) > 2^64. - _Amiram Eldar_, Nov 09 2023
%H A141629 Amiram Eldar, <a href="/A141629/a141629.txt">Table of n, a(n) for n = 1..1000, with zeros for 277 unknown values that are > 2^64</a>.
%H A141629 Vladimir Shevelev, <a href="http://arxiv.org/abs/0807.1975">An upper estimate for the overpseudoprime counting function</a>, arXiv:0807.1975 [math.NT], 2008.
%Y A141629 Cf. A141232, A122929, A140452, A140797, A140803.
%K A141629 nonn,more
%O A141629 1,1
%A A141629 _Vladimir Shevelev_, Aug 24 2008
%E A141629 a(4) corrected and a(12)-a(24) added by _Amiram Eldar_, Nov 09 2023