A143539 Number of ways to express 2n-1 as p+2a^2; p prime, a > 0.

0, 0, 1, 1, 1, 1, 2, 2, 0, 2, 3, 1, 3, 1, 1, 3, 1, 2, 3, 3, 1, 2, 3, 1, 4, 2, 1, 5, 1, 1, 5, 3, 1, 2, 4, 1, 3, 4, 2, 5, 3, 1, 4, 2, 2, 6, 2, 1, 3, 2, 3, 5, 4, 1, 5, 5, 1, 6, 3, 2, 5, 1, 2, 2, 4, 3, 5, 4, 0, 7, 4, 1, 6, 3, 1, 5, 2, 2, 5, 6, 1, 2, 5, 2, 7, 4, 2, 6, 2, 2, 9, 2, 3, 4, 4, 2, 2, 4, 1, 9, 5, 3, 5, 5, 3

Offset: 1

Author

T. D. Noe, Aug 23 2008

Keywords

• nonn

Comments

Similar to A046921 and A046923. Sequence A060003 lists the odd numbers having no representations.

Examples

			a(11)=3 because 21 = 19+2*1^2 = 13+2*2^2 = 3+2*3^2.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000
• L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.

Programs

Mathematica

Table[cnt=0; Do[If[PrimeQ[n-2*k^2], cnt++ ], {k,Floor[Sqrt[n/2]]}]; cnt, {n,1,20000,2}]