A070773 Number of solutions to p(2m)-2p(m)=2n-1, where p(m) = m-th prime.

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, 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, 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

Offset

1,8

Comments

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

Links

Table of n, a(n) for n=1..105.

Example

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.

Mathematica

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*)

Crossrefs

Cf. A066066, A022457, A070774, A069890.

Sequence in context: A103514 A324123 A016570 * A046804 A263211 A287571

Adjacent sequences: A070770 A070771 A070772 * A070774 A070775 A070776

Keyword

nonn

Author

Labos Elemer, May 06 2002

Status

approved