

A247790


Primes p such that sigma(sigma(2p1)) is a prime.


5




OFFSET

1,1


COMMENTS

The next term, if it exists, must be greater than 5*10^7.
Primes p such that A247954(p) = A000203(A000203(2p1)) = A000203(A008438(p1)) = A051027(2p1) 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


LINKS

Table of n, a(n) for n=1..4.


EXAMPLE

Prime 2 is in the sequence because sigma(sigma(2*21)) = sigma(sigma(3)) = sigma(4) = 7, i.e., prime.


MAPLE

with(numtheory): A247790:=n>`if`(isprime(n) and isprime(sigma(sigma(2*n1))), n, NULL): seq(A247790(n), n=1..130000); # Wesley Ivan Hurt, Oct 17 2014


PROG

(MAGMA) [p: p in PrimesUpTo(50000000)  IsPrime(SumOfDivisors(SumOfDivisors(2*p1)))]
(PARI) forprime(p=1, 10^7, if(ispseudoprime(sigma(sigma(2*p1))), print1(p, ", "))) \\ Derek Orr, Sep 29 2014


CROSSREFS

Cf. A000203, A008438, A247791, A247820, A247821, A247822, A247823, A247954.
Sequence in context: A133857 A232869 A153912 * A233460 A324164 A047076
Adjacent sequences: A247787 A247788 A247789 * A247791 A247792 A247793


KEYWORD

nonn,more


AUTHOR

Jaroslav Krizek, Sep 28 2014


EXTENSIONS

a(4) from Giovanni Resta, Feb 14 2020


STATUS

approved



