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

1,13

Comments

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

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

A217892 and A194600 give indices and values of the records.

References

Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comput. 29 (1975), 79-81.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Brier Number

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A194600, A194603, A194606, A194607, A194608, A194635, A194636, A194637, A194638, A194639.

Cf. A040081, A040076, A076335, A180247.

Sequence in context: A266909 A276491 A035177 * A070105 A111397 A131743

Adjacent sequences: A194588 A194589 A194590 * A194592 A194593 A194594

Keyword

sign

Author

Arkadiusz Wesolowski, Aug 29 2011

Status

approved