A098041 Arithmetic mean of successive Mersenne primes.

5, 19, 79, 4159, 69631, 327679, 1074003967, 1152921505680588799, 309485010974266573331628031, 81129947899616503040857729925119, 85070672859873030472525347646947196927

Offset

1,1

Comments

Sequence is based on the following (false) conjecture Shanks mentions in his paper (p.6), which someone else made: "If M_p1 and M_p2 are successive Mersenne primes, their arithmetic mean is also prime." The first four values in the sequence are prime, while the rest up to (2^756839-1 + 2^216091-1)/2 are not. Conjecture: there are no more primes in this sequence after 4159.

Links

Table of n, a(n) for n=1..11.

D. Shanks, Squfof Notes

Example

a(3)=79 because (31+127)/2 = 79.

Crossrefs

Cf. A000043.

Sequence in context: A125657 A111929 A146030 * A346817 A317131 A149780

Adjacent sequences: A098038 A098039 A098040 * A098042 A098043 A098044

Keyword

nonn

Author

Jason Earls, Oct 24 2004

Status

approved