|
%I #3 Dec 15 2017 17:36:46
%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
| 