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

Author

Ant King, Feb 09 2008

Keywords

• nonn

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

Examples

			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.
		

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.

Crossrefs

Cf. A057192, A076336, A094076.

Extensions

More terms from Arkadiusz Wesolowski, Apr 24 2012