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OFFSET
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1,1
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COMMENT
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509203 has been proved to be a member of the sequence, and is conjectured to be the smallest member. However, as of 2009, there are still several smaller numbers which are candidates and have not yet been ruled out (see links).
Riesel numbers are proved by exhibiting a periodic sequence p of prime divisors with p(k) | n*2^k-1 and disproved by finding prime n*2^k-1. It is conjectured that numbers that cannot be proved Riesel in this way are non-Riesel. However, some numbers resist both proof and disproof.
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REFERENCES
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P. Ribenboim, The Book of Prime Number Records, 2nd. ed., 1989, p. 282.
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LINKS
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R. Ballinger and W. Keller, The Riesel Problem: Definition and Status
Chris Caldwell, Riesel Numbers
Chris Caldwell, Sierpinski Numbers
Yves Gallot, A search for some small Brier numbers, 2000.
Tanya Khovanova, Non Recursions
Joe McLean, Brier Numbers
C. Rivera, Brier numbers
Eric Weisstein's World of Mathematics, Riesel numbers
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CROSSREFS
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Cf. A076336, A076335, A003261, A052333, A101036.
Sequence in context: A145539 A157759 A124945 this_sequence A101036 A123321 A147574
Adjacent sequences: A076334 A076335 A076336 this_sequence A076338 A076339 A076340
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KEYWORD
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nonn,bref,hard,more,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 07 2002
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EXTENSIONS
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Normally I require at least four terms but I am making an exception for this one in view of its importance. - N. J. A. Sloane (njas(AT)research.att.com), Nov 07, 2002. See A101036 for the most likely extension.
Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 13 2009
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