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%I #30 May 06 2024 01:43:36
%S 6,28,33550336,137438691328
%N Perfect numbers k such that k+1 is prime.
%C Joerg Arndt checked that up to exponent r=110503 of the corresponding Mersenne prime 2^r - 1 the number n=2^(r-1)*(2^r -1) is not pseudoprime.
%C The listed perfect numbers have exponents r in 2,3,13,19.
%H MathOverflow, <a href="http://mathoverflow.net/questions/62797/even-perfect-numbers-n-with-n1-prime">Even perfect numbers n with n+1 prime</a>.
%F a(n) = A061644(n) - 1. - _Amiram Eldar_, May 06 2024
%e We have a(3) = 33550336 since 33550337 is prime and there is no other such perfect number less than a(3) and that exceeds a(2) = 28.
%o (PARI)
%o {e=[2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787];} /* exponents of Mersenne primes */
%o for(n=1,#e,p=(2^e[n]-1)*(2^(e[n]-1));if(ispseudoprime(p+1),print1(p,", ")));
%Y Cf. A000396, A061644, A099057.
%K nonn,bref,hard,more
%O 1,1
%A _Luis H. Gallardo_, Apr 23 2011