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Smallest prime either of the form n*2^k - 1 or n*2^k + 1, k >= 0, or 0 if no such prime exists.
13

%I #25 Jun 03 2015 18:37:10

%S 2,3,2,3,11,5,13,7,17,11,23,11,53,13,29,17,67,17,37,19,41,23,47,23,

%T 101,53,53,29,59,29,61,31,67,67,71,37,73,37,79,41,83,41,173,43,89,47,

%U 751,47,97,101,101,53,107,53,109,113,113,59,1889,59,487,61,127

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

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

%C Many of these terms are in A093868.

%H Arkadiusz Wesolowski, <a href="/A194603/b194603.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%t 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 *)

%t 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 *)

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

%Y Cf. A038699, A050921, A076335, A180247.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Aug 30 2011