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A098041 Arithmetic mean of successive Mersenne primes. 0
5, 19, 79, 4159, 69631, 327679, 1074003967, 1152921505680588799, 309485010974266573331628031, 81129947899616503040857729925119, 85070672859873030472525347646947196927 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 14:38 EDT 2021. Contains 347668 sequences. (Running on oeis4.)