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A101036 Riesel numbers (n such that n*2^k - 1 is composite for all k >= 1), under the unproved assumption that a Riesel number can be certified by finding a periodic sequence p of prime divisors with p(k) | n*2^k-1. 28
509203, 762701, 777149, 790841, 992077, 1106681, 1247173, 1254341, 1330207, 1330319, 1715053, 1730653, 1730681, 1744117, 1830187, 1976473, 2136283, 2251349, 2313487, 2344211, 2554843, 2924861, 3079469, 3177553, 3292241, 3419789, 3423373, 3580901 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: there are infinitely many Riesel numbers that do not arise from a covering system. See page 16 of the Filaseta et al. reference. - Arkadiusz Wesolowski, Nov 17 2014

a(1) = 509203 is also the smallest odd n for which either n^p*2^k - 1 or abs(n^p - 2^k) is composite for every k > 0 and every prime p > 3. - Arkadiusz Wesolowski, Oct 12 2015

LINKS

Pierre CAMI and Arkadiusz Wesolowski, Table of n, a(n) for n = 1..15000 (P. CAMI supplied the first 335 terms)

M. Filaseta et al., On Powers Associated with Sierpinski Numbers, Riesel Numbers and Polignac’s Conjecture, Journal of Number Theory, Volume 128, Issue 7, July 2008, Pages 1916-1940.

CROSSREFS

See A076337 for references and additional information. Cf. A076336.

Sequence in context: A271583 A076337 A258154 * A244070 A206430 A182296

Adjacent sequences:  A101033 A101034 A101035 * A101037 A101038 A101039

KEYWORD

nonn

AUTHOR

David W. Wilson, Jan 17 2005

EXTENSIONS

Up to 3292241, checked by Don Reble (djr(AT)nk.ca), Jan 17 2005, who comments that up to this point each n*2^k-1 has a prime factor <= 241.

STATUS

approved

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Last modified February 25 10:51 EST 2017. Contains 282599 sequences.