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%I #29 Sep 08 2022 08:46:17
%S 5,11,139,170141183460469231731687303715884105979
%N Primes that are equal to the sum of the prime factors of some perfect number.
%C Primes of the form 2^n + 2*n - 3 such that 2^n - 1 is also prime.
%C Conjectures (defining x = 170141183460469231731687303715884105727 = A007013(4)):
%C (1) 2^x + 2*x - 3 is in this sequence;
%C (2) a(5) = 2^x + 2*x - 3 (see comments of A276493);
%C (3) primes of A007013 are Mersenne prime exponents A000043, i.e., x is new exponent in A000043.
%e a(1) = 5 because 2^2-1 = 3 and 2^2+2*2-3 = 5 are primes,
%e a(2) = 11 because 2^3-1 = 7 and 2^3+2*3-3 = 11 are primes,
%e a(3) = 139 because 2^7-1 = 127 and 2^7+2*7-3 = 139 are primes.
%p A276511:=n->`if`(isprime(2^n-1) and isprime(2^n+2*n-3), 2^n+2*n-3, NULL): seq(A276511(n), n=1..10^3); # _Wesley Ivan Hurt_, Sep 07 2016
%o (Magma) [2^n+2*n-3: n in [1..200] | IsPrime(2^n-1) and IsPrime(2^n+2*n-3)];
%Y Subsequence of A192436.
%Y Cf. A000043, A000396, A000668, A007013, A100118, A276493.
%K nonn,more
%O 1,1
%A _Juri-Stepan Gerasimov_, Sep 06 2016
%E Name suggested by _Michel Marcus_, Sep 07 2016
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