A130504 Number of k for which T(n) + T(k) is prime, with 0<=k<=n and triangular number T(n)=n(n+1)/2.

0, 1, 1, 1, 2, 0, 1, 3, 1, 1, 2, 1, 1, 4, 0, 1, 8, 2, 3, 4, 1, 3, 7, 3, 0, 4, 3, 3, 6, 2, 1, 6, 2, 3, 6, 2, 3, 7, 4, 2, 8, 2, 4, 7, 2, 3, 15, 5, 3, 6, 2, 5, 13, 5, 1, 6, 2, 3, 21, 3, 3, 14, 3, 6, 7, 2, 5, 15, 6, 3, 6, 5, 9, 15, 4, 3, 12, 3, 6, 18, 3, 7, 16, 4, 6, 7, 7, 5, 15, 1, 4, 17, 5, 6, 9, 7, 8, 18, 6, 5

Offset: 0

Author

T. D. Noe, Jun 04 2007

Keywords

• nonn

Comments

It appears that a(n)=0 for n=0,5,14,24 only. See A129634 for the least k.

Examples

			a(4)=2 because 10+1 and 10+3 are prime; a(7)=3 because 28+1, 28+3 and 28+15 are primes.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A069004 (for square numbers).

Programs

Mathematica

nn=100; tri=Range[0,nn]Range[nn+1]/2; Table[cnt=0; Do[If[PrimeQ[tri[[k]]+tri[[n]]], cnt++ ], {k,n}]; cnt, {n,Length[tri]}]