A125130 Successive sums of consecutive primes that form a triangular grid.

2, 10, 41, 129, 328, 712, 1371, 2427, 4028, 6338, 9523, 13887, 19580, 26940, 36227, 47721, 61910, 79168, 99685, 124211, 153178, 186914, 225831, 271061, 322858, 382038, 448869, 524451, 608914, 704204, 810459, 927883, 1057828, 1201162

Offset: 1

Author

Cino Hilliard, Jan 10 2007

Keywords

• easy
• nonn

Examples

			The consecutive primes 2, 3, 5, 7, 11, 13 form the triangular grid
     2
   3  5
  7 11 13
These consecutive primes add up to 41, the third entry in the table.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217, A007504, A078721.

Partial sums of A007468.

Programs

Mathematica

With[{nmax = 50}, Accumulate[Prime[Range[PolygonalNumber[nmax]]]][[PolygonalNumber[Range[nmax]]]]] (* Paolo Xausa, May 15 2025 *)

PARI

a(n) = sum(x=1, n*(n+1)/2, prime(x))

Formula

a(n) ~ x^2/(2*log(x)-1), where x = prime(n*(n-1)/2+n). For n = 10000, the relative error is about 0.06%.

a(n) = A007504(A000217(n)). - Andrew Howroyd, Sep 28 2024