A194603 Smallest prime either of the form n*2^k - 1 or n*2^k + 1, k >= 0, or 0 if no such prime exists.

2, 3, 2, 3, 11, 5, 13, 7, 17, 11, 23, 11, 53, 13, 29, 17, 67, 17, 37, 19, 41, 23, 47, 23, 101, 53, 53, 29, 59, 29, 61, 31, 67, 67, 71, 37, 73, 37, 79, 41, 83, 41, 173, 43, 89, 47, 751, 47, 97, 101, 101, 53, 107, 53, 109, 113, 113, 59, 1889, 59, 487, 61, 127

Offset

1,1

Comments

Primes arising from A194591 (or 0 if no such prime exists).

Many of these terms are in A093868.

Links

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

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)=13.

Mathematica

Table[k = 0; While[! PrimeQ[a = n*2^k - 1] && ! PrimeQ[a = n*2^k + 1], k++]; a, {n, 100}] (* Arkadiusz Wesolowski, Sep 04 2011 *)
n2k[n_]:=Module[{k=0}, While[NoneTrue[n*2^k+{1, -1}, PrimeQ], k++]; SelectFirst[ n*2^k+{-1, 1}, PrimeQ]]; Array[n2k, 70] (* The program uses the NoneTrue and SelectFirst functions from Mathematica version 10 *) (* Harvey P. Dale, Jun 03 2015 *)

Crossrefs

Cf. A194591, A194600, A194606, A194607, A194608, A194635, A194636, A194637, A194638, A194639.

Cf. A038699, A050921, A076335, A180247.

Sequence in context: A251090 A078331 A093868 * A183465 A223168 A322404

Adjacent sequences: A194600 A194601 A194602 * A194604 A194605 A194606

Keyword

nonn

Author

Arkadiusz Wesolowski, Aug 30 2011

Status

approved