A187716 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}.

21484572547591559649, 50166404682516122859, 51814002736113272553, 53246606581410442023, 58992081042572747991, 65634687179877002283, 80269357428943941837, 92027572854849003627, 103083799330841020677

Offset: 1

Author

Arkadiusz Wesolowski, Mar 17 2011

Keywords

• nonn

Comments

Wilfrid Keller (2004, published) gave the first known example.

21484572547591559649 computed in 2017 by the author.

Conjecture: 21484572547591559649 is the smallest Sierpiński number that is divisible by 3. - Arkadiusz Wesolowski, May 12 2017

The above conjecture is false, because the Sierpiński number 7592506760633776533 is a counterexample. - Arkadiusz Wesolowski, Jul 27 2023

Links

• Chris Caldwell, The Prime Glossary, Sierpinski number
• Carlos Rivera, Problem 49. Sierpinski-like numbers, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A076336, A187714.

Extensions

Name changed and entry revised by Arkadiusz Wesolowski, May 11 2017