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%I #44 Sep 08 2022 08:46:09
%S 2,28669,126961,500461553802019261
%N Primes p such that sigma(sigma(2p-1)) is a prime.
%C The next term, if it exists, must be greater than 5*10^7.
%C Primes p such that A247954(p) = A000203(A000203(2p-1)) = A000203(A008438(p-1)) = A051027(2p-1) is a prime q. The corresponding values of the primes q are: 7, 131071, 524287, ... (A247791). Conjecture: the primes q are Mersenne primes (A000668).
%C Conjecture: the next term is 500461553802019261 (see comment from _Hiroaki Yamanouchi_ in A247821). - _Jaroslav Krizek_, Oct 08 2014
%C These are the primes in A247821. - _M. F. Hasler_, Oct 14 2014
%C No other terms up to 5*10^10. - _Michel Marcus_, Feb 11 2020
%C a(5) > 5*10^18. - _Giovanni Resta_, Feb 14 2020
%e Prime 2 is in the sequence because sigma(sigma(2*2-1)) = sigma(sigma(3)) = sigma(4) = 7, i.e., prime.
%p with(numtheory): A247790:=n->`if`(isprime(n) and isprime(sigma(sigma(2*n-1))),n,NULL): seq(A247790(n), n=1..130000); # _Wesley Ivan Hurt_, Oct 17 2014
%o (Magma) [p: p in PrimesUpTo(50000000) | IsPrime(SumOfDivisors(SumOfDivisors(2*p-1)))]
%o (PARI) forprime(p=1,10^7,if(ispseudoprime(sigma(sigma(2*p-1))),print1(p,", "))) \\ _Derek Orr_, Sep 29 2014
%Y Cf. A000203, A008438, A247791, A247820, A247821, A247822, A247823, A247954.
%K nonn,more
%O 1,1
%A _Jaroslav Krizek_, Sep 28 2014
%E a(4) from _Giovanni Resta_, Feb 14 2020
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