A130504 -id:A130504 - cp's OEIS frontend

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

Jonathan Vos Post, May 31 2007

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

			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.

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

Cf. A000040, A000217, A129755, A130334.

Cf. A069003 (for square numbers).

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 *)

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}.

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

A209777 Number of q in the range 0<=q<=n for which k(n)+k(q) is prime, with k(n) := n*(n+1)^2/2.

Original entry on oeis.org

1, 1, 0, 1, 0, 2, 1, 0, 0, 3, 0, 1, 2, 0, 0, 2, 1, 3, 1, 0, 0, 9, 1, 0, 2, 2, 0, 2, 1, 2, 4, 0, 0, 6, 1, 1, 5, 4, 1, 3, 2, 3, 2, 0, 0, 15, 0, 2, 2, 3, 3, 7, 1, 4, 2, 1, 3, 17, 2, 1, 6, 5, 1, 4, 2, 8, 3, 0, 0, 7, 2, 3, 9, 3, 1, 2, 0, 9, 1, 0, 2, 21, 1, 4, 6, 9, 2, 5, 2, 4, 6, 3, 3, 16, 2, 2, 4, 5, 1, 2

Offset: 1

Gerasimov Sergey, Mar 27 2012

nonn

			a(6)=2 because 147+2 and 147+50 are primes;
a(10)=3 because 605+2, 605+224 and 605+324 are primes.

Cf. A006002, A130504.

Corrected by R. J. Mathar, Mar 30 2012

cp's OEIS Frontend

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

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