

A098041


Arithmetic mean of successive Mersenne primes.


0



5, 19, 79, 4159, 69631, 327679, 1074003967, 1152921505680588799, 309485010974266573331628031, 81129947899616503040857729925119, 85070672859873030472525347646947196927
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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 (2^7568391 + 2^2160911)/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



