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A098041 Arithmetic mean of successive Mersenne primes. 0


%S 5,19,79,4159,69631,327679,1074003967,1152921505680588799,

%T 309485010974266573331628031,81129947899616503040857729925119,

%U 85070672859873030472525347646947196927

%N Arithmetic mean of successive Mersenne primes.

%C 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.

%H D. Shanks, <a href="http://cadigweb.ew.usna.edu/%7ewdj/mcmath/shanks_squfof.pdf">Squfof Notes</a>

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

%Y Cf. A000043.

%K nonn

%O 1,1

%A _Jason Earls_, Oct 24 2004

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Last modified October 25 11:11 EDT 2021. Contains 348243 sequences. (Running on oeis4.)