A137715 Prime values of n for which n*2^k + 1 is composite for all positive integers k.

271129, 322523, 327739, 482719, 934909, 1639459, 2131043, 2131099, 2576089, 3098059, 3608251, 4573999, 6678713, 6799831, 7523281, 7761437, 8184977, 8840599, 8879993, 8959163, 9208337, 9252323, 9930469, 9937637, 10192733, 10306187, 10391933, 11206501

Offset

1,1

Comments

The sequence contains those members of A076336 that are prime.

Note that the terms in A076336 are presently conjectural. - Joerg Arndt, Jun 29 2015

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..3670

R. Baillie, G. Cormack, and H. C. Williams, The Problem of Sierpinski Concerning k*2^n+1, Mathematics of Computation, Vol. 37, No. 155 (July 1981), pp. 229-231. Corrigenda; Mathematics of Computation, Vol. 39, No. 159 (July 1982), p. 308.

Wilfrid Keller, Factors of Fermat Numbers and Large Primes of the Form k*2^n+1, Mathematics of Computation, Vol. 41, No. 164 (October 1983), pp. 661-673.

Mersenne Forum, The Prime Sierpinski Problem.

Seventeen or Bust, A Distributed Attack on the Sierpinski problem

W. Sierpinski, Sur un problème concernant les nombres k*2^n+1, Elem. d. Math. 15, pp. 73-74, 1960.

Example

As 271129 is the first known prime value of n for which n*2^k + 1 is composite for all positive integers k, a(1) = 271129.

Crossrefs

Cf. A057192, A076336, A094076.

Sequence in context: A257647 A206001 A244561 * A258893 A237181 A013998

Adjacent sequences: A137712 A137713 A137714 * A137716 A137717 A137718

Keyword

nonn

Author

Ant King, Feb 09 2008

Extensions

More terms from Arkadiusz Wesolowski, Apr 24 2012

Status

approved