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Search: id:A006517
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| A006517 |
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Numbers n such that n divides 2^n + 2.
(Formerly M1719)
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+0
3
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| 1, 2, 6, 66, 946, 8646, 180246, 199606, 265826, 383846, 1234806, 3757426, 9880278, 14304466, 23612226, 27052806, 43091686, 63265474, 66154726, 69410706, 81517766, 106047766, 129773526, 130520566, 149497986, 184416166, 279383126
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All terms greater than 1 are even. If an odd term n>1 exists then n = m*2^k + 1 for some k>=1 and odd m. Then n divides 2^(m*2^k) + 1 and so does every prime factor p of n, implying that 2^(k+1) divides the multiplicative order of 2 modulo p and thus p-1. Therefore n = m*2^k + 1 is the product of prime factors of the form t*2^(k+1) + 1, implying that n-1 is divisible by 2^(k+1), a contradiction. [From Max Alekseyev (maxale(AT)gmail.com), Mar 16 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. Honsberger, Mathematical Gems, M.A.A., 1973, p. 142.
Sierpinski, W. 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970. Problem #18
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MATHEMATICA
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Do[ If[ PowerMod[ 2, n, n ] + 2 == n, Print[n]], {n, 2, 1500000000, 4} ]
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CROSSREFS
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Cf. A006521.
Sequence in context: A046399 A082619 A082617 this_sequence A091458 A087331 A097419
Adjacent sequences: A006514 A006515 A006516 this_sequence A006518 A006519 A006520
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Corrected and extended by Joe K. Crump (joecr(AT)carolina.rr.com), Sep 12 2000 and Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 13 2000
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