A070773 - OEIS

%I #5 Oct 15 2013 22:31:19

%S 1,1,1,1,1,1,1,3,1,2,2,0,1,0,2,1,1,3,1,1,0,1,2,0,2,1,1,1,3,2,1,3,0,1,

%T 2,2,0,0,0,0,2,1,0,3,0,3,2,3,3,1,0,0,2,2,3,2,0,3,1,0,1,1,0,1,1,1,1,7,

%U 1,2,2,1,1,1,1,2,1,0,2,0,0,2,0,1,0,1,1,0,1,0,1,0,1,1,2,2,3,3,2,1,2,1,2,2,4

%N Number of solutions to p(2m)-2p(m)=2n-1, where p(m) = m-th prime.

%C p(2m)-2p(m) is approximately 2m Log[2].

%e n=12: 2n-1=23, no solution, so a(12)=0; n=8: 2n-1=15, p[2x]={53,61,89},2*p(x)=2*{19,23,37}={38,46,74}, p[2x]-2p[x]={15,15,15}, three solutions, so a(8)=3.

%t j=0; Table[Print[j]; j=0; Do[s=Prime[2*n]-2*Prime[n]; If[Equal[s, 2*k-1], j=j+1], {n, 1, 2*k}], {k, 1, 11000}] (*number of solution=j*)

%Y Cf. A066066, A022457, A070774, A069890.

%K nonn

%O 1,8

%A _Labos Elemer_, May 06 2002