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Search: id:A098041
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| A098041 |
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Arithmetic mean of successive Mersenne primes. |
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+0
1
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| 5, 19, 79, 4159, 69631, 327679, 1074003967, 1152921505680588799, 309485010974266573331628031, 81129947899616503040857729925119, 85070672859873030472525347646947196927
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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D. Shanks, Squfof Notes
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EXAMPLE
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a(3)=79 because (31+127)/2 = 79.
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CROSSREFS
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Cf. A000043.
Sequence in context: A125657 A111929 A146030 this_sequence A149780 A149781 A149782
Adjacent sequences: A098038 A098039 A098040 this_sequence A098042 A098043 A098044
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KEYWORD
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nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Oct 24 2004
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