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A076337 Riesel numbers: n such that for all k >= 1 the numbers n*2^k - 1 are composite. +0
6
509203 (list; graph; listen)
OFFSET

1,1

COMMENT

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.

REFERENCES

P. Ribenboim, The Book of Prime Number Records, 2nd. ed., 1989, p. 282.

LINKS

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

CROSSREFS

Cf. A076336, A076335, A003261, A052333, A101036.

Sequence in context: A082248 A145539 A124945 this_sequence A101036 A123321 A147574

Adjacent sequences: A076334 A076335 A076336 this_sequence A076338 A076339 A076340

KEYWORD

nonn,bref,hard,more

AUTHOR

njas, Nov 07 2002

EXTENSIONS

Normally I require at least four terms but I am making an exception for this one in the hope that someone will extend it. - njas, Nov 07, 2002. See A101036 for the most likely extension.

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Last modified December 3 14:12 EST 2008. Contains 151279 sequences.


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