A247790 Primes p such that sigma(sigma(2p-1)) is a prime.

2, 28669, 126961, 500461553802019261

Offset: 1

Author

Jaroslav Krizek, Sep 28 2014

Keywords

• nonn
• more

Comments

The next term, if it exists, must be greater than 5*10^7.

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).

Conjecture: the next term is 500461553802019261 (see comment from Hiroaki Yamanouchi in A247821). - Jaroslav Krizek, Oct 08 2014

These are the primes in A247821. - M. F. Hasler, Oct 14 2014

No other terms up to 5*10^10. - Michel Marcus, Feb 11 2020

a(5) > 5*10^18. - Giovanni Resta, Feb 14 2020

Examples

			Prime 2 is in the sequence because sigma(sigma(2*2-1)) = sigma(sigma(3)) = sigma(4) = 7, i.e., prime.
		

Crossrefs

Cf. A000203, A008438, A247791, A247820, A247821, A247822, A247823, A247954.

Programs

Magma

[p: p in PrimesUpTo(50000000) | IsPrime(SumOfDivisors(SumOfDivisors(2*p-1)))]

Maple

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

PARI

forprime(p=1,10^7,if(ispseudoprime(sigma(sigma(2*p-1))),print1(p,", "))) \\ Derek Orr, Sep 29 2014

Extensions

a(4) from Giovanni Resta, Feb 14 2020