
OFFSET

1,1


COMMENTS

509203 has been proved to be a member of the sequence, and is conjectured to be the smallest member. However, as of 2009, there are still several smaller numbers which are candidates and have not yet been ruled out (see links).
Riesel numbers are proved by exhibiting a periodic sequence p of prime divisors with p(k)  n*2^k1 and disproved by finding prime n*2^k1. It is conjectured that numbers that cannot be proved Riesel in this way are nonRiesel. However, some numbers resist both proof and disproof.
Others conjecture the opposite: that there are infinitely many Riesel numbers that do not arise from a covering system, see A101036. The word "odd" is needed in the definition because otherwise for any term n, all numbers n*2^m, m >= 1, would also be Riesel numbers, but we don't want them in this sequence (as is manifest from A101036). Since 1 and 3 obviously are not in this sequence, for any n in this sequence n1 is an even number > 2 and therefore composite, so one could replace "k >= 1" equivalently by "k >= 0".  M. F. Hasler, Aug 20 2020
Named after the Swedish mathematician Hans Ivar Riesel (19292014).  Amiram Eldar, Apr 02 2022


REFERENCES

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


LINKS



CROSSREFS



KEYWORD

nonn,bref,hard,more


AUTHOR



EXTENSIONS

Normally I require at least four terms but I am making an exception for this one in view of its importance.  N. J. A. Sloane, Nov 07 2002. See A101036 for the most likely extension.
Definition corrected ("odd" added) by M. F. Hasler, Aug 23 2020


STATUS

approved

