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A098041
Arithmetic mean of successive Mersenne primes.
0
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.
EXAMPLE
a(3)=79 because (31+127)/2 = 79.
CROSSREFS
Cf. A000043.
Sequence in context: A125657 A111929 A146030 * A346817 A317131 A149780
KEYWORD
nonn
AUTHOR
Jason Earls, Oct 24 2004
STATUS
approved