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A247791
Primes p such that there is a prime q for which sigma(sigma(2q-1)) = p.
5
7, 131071, 524287
OFFSET
1,1
COMMENTS
The next term, if it exists, must be greater than 5*10^7.
Primes p such that there is prime q for which sigma(sigma(2q-1)) = A247954(q) = A000203(A000203(2q-1)) = A000203(A008438(q-1)) = A051027(2q-1) = p.
Corresponding values of primes q: 2, 28669, 126961, ... (A247790).
Conjecture: Subsequence of Mersenne primes.
Conjecture: the next term is 2305843009213693951 when 2305843009213693951 = sigma(sigma(2*500461553802019261-1)) where 500461553802019261 is prime (see comment of Hiroaki Yamanouchi in A247821). - Jaroslav Krizek, Oct 08 2014
EXAMPLE
Prime 7 is in sequence because there is prime 2 such that sigma(sigma(2*2-1)) = sigma(sigma(3)) = sigma(4) = 7.
PROG
(Magma)[SumOfDivisors(SumOfDivisors(2*n-1)): n in [A247790(n)]
(Magma)[SumOfDivisors(SumOfDivisors(2*n-1)): n in[1..1000000] | IsPrime(SumOfDivisors(SumOfDivisors(2*n-1))) and IsPrime(n)]
(PARI)
forprime(p=1, 10^7, if(ispseudoprime(sigma(sigma(2*p-1))), print1(sigma(sigma(2*p-1)), ", "))) \\ Derek Orr, Sep 29 2014
KEYWORD
nonn,more,bref
AUTHOR
Jaroslav Krizek, Sep 28 2014
STATUS
approved