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A076335
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Brier numbers: both Riesel and Sierpinski, or odd n such that for all k >= 1 the numbers n*2^k + 1 and n*2^k - 1 are composite.
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16
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OFFSET
| 1,1
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COMMENTS
| These are just the smallest examples known - there may be smaller ones.
143665583045350793098657 computed in 2007 by Michael Filaseta, Carrie Finch, Mark Kozek. See http://www.math.sc.edu/~filaseta/papers/SierpinskiEtCoPapNew.pdf.
There are no Brier numbers below 10^9. [From Arkadiusz Wesolowski, Aug 03 2009]
17830557039648116519025581 computed in 2010 by Arkadiusz Wesolowski. [Arkadiusz Wesolowski, Jan 12 2011]
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REFERENCES
| Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comput. 29 (1975), 79-81.
P. Erdos, On integers of the form 2^k + p and some related problems, Summa Brasil. Math. 2 (1950), 113-123.
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LINKS
| Chris Caldwell, Riesel Numbers
Chris Caldwell, Sierpinski Numbers
Yves Gallot, A search for some small Brier numbers, 2000.
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 6992565235279559197457863
Joe McLean, Brier Numbers [Cached copy]
Carlos Rivera, See here for latest information about progress on this sequence
Carlos Rivera, Problem 29 [From Carlos Rivera (cbrfgm(AT)gmail.com), May 30 2010]
Eric Weisstein's World of Mathematics, Brier Number
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CROSSREFS
| Cf. A194591, A194600, A194603, A194606, A194607, A194608, A194635, A194636, A194637, A194638, A194639, A076336, A076337, A040081, A040076, A103963, A103964, A038699, A050921, A064699, A052333, A003261.
Cf. A180247 gives the primes.
Sequence in context: A008916 A105299 A094232 * A132185 A003942 A003935
Adjacent sequences: A076332 A076333 A076334 * A076336 A076337 A076338
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KEYWORD
| bref,nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com), Nov 07 2002
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EXTENSIONS
| Many terms reported in the Problem 29 from "The Prime Problems & Puzzles Connection" Carlos Rivera (cbrfgm(AT)gmail.com), May 30 2010
Entry revised by Arkadiusz Wesolowski, Jan 12 2011
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