A194636 Least k >= 0 such that (2*n-1)*2^k - 1 or (2*n-1)*2^k + 1 is prime, or -1 if no such value exists.

0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 5, 3, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 3, 6, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 5, 1, 3, 4, 1, 1, 1, 1, 2, 2, 1, 4, 1, 2

Offset

1,7

Comments

Bisection of A194591: a(n) = A194591(2*n-1).

A194637 gives the record values.

Links

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

Eric Weisstein's World of Mathematics, Brier Number

Example

For n=4, 7*2^0-1 and 7*2^0+1 are composite, but 7*2^1-1=13 is prime, so a(4)=1.

Mathematica

Table[n = 2*n - 1; k = 0; While[! PrimeQ[n*2^k - 1] && ! PrimeQ[n*2^k + 1], k++]; k, {n, 100}] (* Arkadiusz Wesolowski, Sep 04 2011 *)
p[n_]:=Module[{c=2n-1, k=0}, While[!Or@@PrimeQ[c*2^k+{1, -1}], k++]; k]; Array[ p, 90] (* Harvey P. Dale, Mar 08 2013 *)

Crossrefs

Cf. A194591, A194600, A194603, A194606, A194607, A194608, A194635, A194637, A194638, A194639.

Cf. A040081, A040076, A076335, A180247.

Sequence in context: A106345 A319395 A374462 * A286299 A081729 A219157

Adjacent sequences: A194633 A194634 A194635 * A194637 A194638 A194639

Keyword

sign

Author

Arkadiusz Wesolowski, Aug 31 2011

Status

approved