A189373 Perfect numbers n such that n+1 is prime.

6, 28, 33550336, 137438691328

Offset

1,1

Comments

Joerg Arndt checked that up to exponent r=110503 of the corresponding Mersenne prime 2^r - 1 the number n=2^(r-1)*(2^r -1) is not pseudoprime.

The listed perfect numbers have exponents r in 2,3,13,19.

Links

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

MathOverflow, Even perfect numbers n with n+1 prime

Example

We have a(3)=33550336 since 33550337 is prime and there is no other such perfect number less than a(3) and that exceeds a(2)=28.

Prog

(PARI)
{e=[2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787]; } /* exponents of Mersenne primes */
for(n=1, #e, p=(2^e[n]-1)*(2^(e[n]-1)); if(ispseudoprime(p+1), print1(p, ", ")));

Crossrefs

Cf. A099057.

Sequence in context: A330163 A276493 A074849 * A156927 A178366 A175956

Adjacent sequences: A189370 A189371 A189372 * A189374 A189375 A189376

Keyword

nonn,bref,hard,more

Author

Luis H. Gallardo, Apr 23 2011

Status

approved