A194591 Least k >= 0 such that n*2^k - 1 or n*2^k + 1 is prime, or -1 if no such value exists.

0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 5, 0, 3, 0, 1, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 1, 2, 0, 1, 0, 1, 0, 1, 0, 4, 1

Offset: 1

Author

Arkadiusz Wesolowski, Aug 29 2011

Keywords

• sign

Comments

Fred Cohen and J. L. Selfridge showed that a(n) = -1 infinitely often.

a(n) = 0 iff n is in A045718.

Examples

			For n=7, 7*2^0-1 and 7*2^0+1 are composite, but 7*2^1-1=13 is prime, so a(7)=1.
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
• Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comp. 29 (1975), 79-81.
• Eric Weisstein's World of Mathematics, Brier Number

Crossrefs

Cf. A194603, A194606, A194607, A194608, A194635, A194636, A194637, A194638, A194639.

Cf. A040081, A040076, A076335, A180247.

Cf. A217892 and A194600 (indices and values of the records).

Programs

Mathematica

Table[k = 0; While[! PrimeQ[n*2^k - 1] && ! PrimeQ[n*2^k + 1], k++]; k, {n, 100}] (* T. D. Noe, Aug 29 2011 *)

Formula

If a(n)>0, then a(2n)=a(n)-1.