A129634 Least nonnegative m such that T(n) + T(m) is prime, where T(n) = n*(n+1)/2.

2, 1, 0, 1, 1, 7, 4, 1, 1, 7, 3, 1, 1, 3, 16, 13, 1, 4, 4, 1, 1, 4, 4, 1, 46, 3, 7, 1, 2, 7, 16, 2, 13, 4, 3, 1, 13, 3, 4, 22, 1, 16, 16, 1, 1, 7, 3, 1, 10, 3, 7, 1, 2, 7, 16, 2, 1, 4, 4, 13, 1, 4, 16, 1, 1, 16, 4, 2, 1, 16, 8, 1, 10, 3, 7, 1, 1, 31, 7, 2, 13, 4, 4, 10, 1, 8, 7, 13, 1, 43, 16, 5, 25, 16

Offset: 0

Author

Jonathan Vos Post, May 31 2007

Keywords

• easy
• nonn

Comments

What is the simplest proof that this is defined for all nonzero n?

It appears that a(n)A130504 provides evidence that a(n) exists for all n. - T. D. Noe, Jun 04 2007

Examples

			a(6) = 4 because T(4) = 10 is the least triangular number whose sum with T(6) = 21 is prime, since {21+0 = 3*7, 21+3 = 2^3*3, 21+6 = 3^3} are all composite, but 21+10 = 31 is prime.
		

Links

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

Crossrefs

Cf. A000040, A000217, A129755, A130334.

Cf. A069003 (for square numbers).

Programs

Mathematica

nn=100; tri=Range[0,nn]Range[nn+1]/2; Table[k=1; While[k<=Length[tri] && !PrimeQ[tri[[k]]+tri[[n]]], k++ ]; If[k<=Length[tri], k-1,0], {n,Length[tri]}] (* T. D. Noe, Jun 04 2007 *)

Formula

a(n) = Min{m: m*(m+1)/2 + n*(n+1)/2 is prime}. a(n) = Min{m: A000217(m) + A000217(n) is an element of A000040}.

Extensions

Corrected and extended by T. D. Noe, Jun 04 2007