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A187716
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Odd numbers m divisible by 3 such that for every k >= 1, m*2^k + 1 has a divisor in the set {5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 109, 151, 241, 331}.
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%I #31 Jul 29 2023 05:02:51
%S 21484572547591559649,50166404682516122859,51814002736113272553,
%T 53246606581410442023,58992081042572747991,65634687179877002283,
%U 80269357428943941837,92027572854849003627,103083799330841020677
%N Odd numbers m divisible by 3 such that for every k >= 1, m*2^k + 1 has a divisor in the set {5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 109, 151, 241, 331}.
%C Wilfrid Keller (2004, published) gave the first known example.
%C 21484572547591559649 computed in 2017 by the author.
%C Conjecture: 21484572547591559649 is the smallest Sierpiński number that is divisible by 3. - _Arkadiusz Wesolowski_, May 12 2017
%C The above conjecture is false, because the Sierpiński number 7592506760633776533 is a counterexample. - _Arkadiusz Wesolowski_, Jul 27 2023
%H Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/SierpinskiNumber.html">Sierpinski number</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/problems/prob_049.htm">Problem 49. Sierpinski-like numbers</a>, The Prime Puzzles & Problems Connection.
%Y Cf. A076336, A187714.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Mar 17 2011
%E Name changed and entry revised by _Arkadiusz Wesolowski_, May 11 2017
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