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

Author

Arkadiusz Wesolowski, Aug 31 2011

Keywords

• sign

Comments

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

A194637 gives the record values.

Examples

			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.
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Brier Number

Crossrefs

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

Cf. A040081, A040076, A076335, A180247.

Programs

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 *)