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A125130
Successive sums of consecutive primes that form a triangular grid.
0
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
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
Partial sums of A007468.
Sequence in context: A127113 A051540 A272135 * A110684 A197175 A297047
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Jan 10 2007
STATUS
approved