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

1,1

Comments

These sums, for a given n, can be estimated by the following formula. sum est = x^2/(2*log(x)-1) Where x = prime(n*(n-1)/2+n) For example, n = 10000 x = 982555543 sum est = 23889718028585418 sum act = 23904330028803899 Relative Error = 0.00061127001680771897

Links

Table of n, a(n) for n=1..34.

Formula

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

Example

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.

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