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

Author

Arkadiusz Wesolowski, Aug 30 2011

Keywords

• nonn

Comments

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

Many of these terms are in A093868.

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)=13.
		

Links

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

Crossrefs

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

Cf. A038699, A050921, A076335, A180247.

Programs

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 *)