# Riesel numbers and others

N. J. A. Sloane njas at research.att.com
Thu Nov 7 17:18:06 CET 2002

```A recent email from Olivier led me to
extending!    Neil

%I A076335
%S A076335 878503122374924101526292469,3872639446526560168555701047,
%T A076335 623506356601958507977841221247
%N A076335 Brier numbers: both Riesel and Sierpinski, or n such that for all k >= 0 the numbers n*2^k + 1 and n*2^k - 1 are composite.
%C A076335 These are just the smallest examples known - there may be smaller ones.
%Y A076335 Cf. A076336, A076337.
%H A076335 Yves Gallot, <a href="http://perso.wanadoo.fr/yves.gallot/papers/smallbrier.html">A search for some small Brier numbers</a>, 2000.
%H A076335 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_029.htm">Brier numbers</a>
%K A076335 nonn,new
%O A076335 1,1
%A A076335 Olivier Gerard (ogerard at ext.jussieu.fr), Nov 07 2002

%I A076336
%S A076336 78557
%N A076336 Riesel numbers: n such that for all k >= 0 the numbers n*2^k + 1 are composite.
%Y A076336 Cf. A076337, A076335, A003261.
%K A076336 nonn,new,bref,hard,more
%H A076336 Yves Gallot, <a href="http://perso.wanadoo.fr/yves.gallot/papers/smallbrier.html">A search for some small Brier numbers</a>, 2000.
%H A076336 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_029.htm">Brier numbers</a>
%O A076336 1,1
%A A076336 njas, Nov 07 2002
%E A076336 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.

%I A076337
%S A076337 509203
%N A076337 Sierpinski numbers: n such that for all k >= 0 the numbers n*2^k - 1 are composite.
%Y A076337 Cf. A076337, A076335.
%K A076337 nonn,new,bref,hard,more
%H A076337 Yves Gallot, <a href="http://perso.wanadoo.fr/yves.gallot/papers/smallbrier.html">A search for some small Brier numbers</a>, 2000.
%H A076337 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_029.htm">Brier numbers</a>
%O A076337 1,1
%A A076337 njas, Nov 07 2002
%E A076337 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.

Neil Sloane

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