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%I #26 May 27 2017 05:26:55
%S 161038,9115426,143742226,665387746,1105826338,3434672242,11675882626,
%T 16732427362,18411253246,81473324626,85898088046,98730252226,
%U 134744844466,136767694402,161097973246,183689075122,315554044786,553588254766,778581406786,1077392692846
%N Fermat pseudoprimes n such that n+1 is prime.
%C Kazimierz Szymiczek asked about the existence of such pseudoprimes in 1972 (Problem 42 in Rotkiewicz's book). Rotkiewicz found the first 6 terms. Rotkiewicz also proved that there is no Fermat pseudoprime n such that n-1 is prime.
%C Subsequence of A006935.
%D Andrzej Rotkiewicz, Pseudoprime Numbers and Their Generalizations, Student Association of the Faculty of Sciences, University of Novi Sad, Novi Sad, Yugoslavia, 1972.
%H Amiram Eldar, <a href="/A287297/b287297.txt">Table of n, a(n) for n = 1..165</a>
%H Andrzej Rotkiewicz, <a href="http://dml.cz/dmlcz/137472">On pseudoprimes having special forms and a solution of K. Szymiczek's problem</a>, Acta Mathematica Universitatis Ostraviensis, Vol. 13, No. 1 (2005), pp. 57-71.
%e 161038 is in the sequence since it is a Fermat pseudoprime (2^161038 == 2 (mod 161038)), and 161038 + 1 = 161039 is prime.
%Y Cf. A001567, A006935, A057942.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 26 2017
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