A125130 - OEIS

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

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OFFSET

1,1

LINKS

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

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

EXAMPLE

The consecutive primes 2, 3, 5, 7, 11, 13 form the triangular grid

3 5

7 11 13

These consecutive primes add up to 41, the third entry in the table.

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A000217, A007504, A078721.

Partial sums of A007468.

Sequence in context: A127113 A051540 A272135 * A110684 A197175 A297047

Adjacent sequences: A125127 A125128 A125129 * A125131 A125132 A125133

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Jan 10 2007

STATUS

approved