%I A134876
%S A134876 1,2,1,3,4,8,18,23,44,73,142,277,484,871,1644,3060,5851,10917,20776,
%T A134876 39263,74752,142521,271223,520242,996486,1916486,3686628,7103236,
%U A134876 13702428,26469008
%N A134876 Number of Proth primes; primes of the form 1 + k*2^n with k odd and k 
               < 2^n.
%C A134876 All primes were found by Mathematica's PrimeQ function and proved using 
               Proth's theorem. The ratio of consecutive terms is about 1.93.
%H A134876 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ProthsTheorem.html">MathWorld: Proth's Theorem</a>
%e A134876 a(1)=1 because 3 is the only Proth prime for n=1. a(2)=2 because 5 and 
               13 are the only primes for n=2. a(3)=1 because 41 is the only prime 
               for n=3.
%t A134876 Table[cnt=0; Do[If[PrimeQ[1+k*2^n], cnt++ ], {k,1,2^n,2}]; cnt, {n,20}]]
%Y A134876 Cf. A080076.
%Y A134876 Sequence in context: A000032 A061084 A055391 this_sequence A019612 A007444 
               A166476
%Y A134876 Adjacent sequences: A134873 A134874 A134875 this_sequence A134877 A134878 
               A134879
%K A134876 nonn
%O A134876 1,2
%A A134876 T. D. Noe (noe(AT)sspectra.com), Nov 17 2007