%I A040076
%S A040076 0,0,1,0,1,0,2,1,1,0,1,0,2,1,1,0,3,0,6,1,1,0,1,2,2,1,2,0,1,0,8,3,1,2,1,
%T A040076 0,2,5,1,0,1,0,2,1,2,0,583,1,2,1,1,0,1,1,4,1,2,0,5,0,4,7,1,2,1,0,2,1,1,
%U A040076 0,3,0,2,1,1,4,3,0,2,3,1,0,1,2,4,1,2,0,1,1,8,7,2,582,1,0,2,1,1,0,3,0
%N A040076 Smallest m >= 0 such that n*2^m+1 is prime, or -1 if no such m exists.
%C A040076 Sierpinski showed that a(n) = -1 infinitely often. John Selfridge showed 
               that a(78557) = -1 and it is conjectured that a(n) >= 0 for all n 
               < 78557.
%H A040076 T. D. Noe, <a href="b040076.txt">Table of n, a(n) for n=1..1000</a>
%H A040076 Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.net/
               sierp.html">The Sierpinski Problem: Definition and Status</a>
%H A040076 Seventeen or Bust, <a href="http://www.seventeenorbust.com/">A Distributed 
               Attack on the Sierpinski problem</a>
%e A040076 1*(2^0)+1=2 is prime, so a(1)=0;
%e A040076 3*(2^1)+1=5 is prime, so a(3)=1;
%e A040076 For n=7, 7+1 and 7*2+1 are composite, but 7*2^2+1=29 is prime, so a(7)=2.
%t A040076 Do[m = 0; While[ !PrimeQ[n*2^m + 1], m++ ]; Print[m], {n, 1, 110} ]
%Y A040076 For the corresponding primes see A050921. Cf. A103964, A040081.
%Y A040076 Sequence in context: A130538 A078659 A079690 this_sequence A019269 A035155 
               A090584
%Y A040076 Adjacent sequences: A040073 A040074 A040075 this_sequence A040077 A040078 
               A040079
%K A040076 nonn,easy,nice
%O A040076 1,7
%A A040076 David W. Wilson (davidwwilson(AT)comcast.net)