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%I #5 Jun 24 2022 19:50:37
%S 2,10,41,129,328,712,1371,2427,4028,6338,9523,13887,19580,26940,36227,
%T 47721,61910,79168,99685,124211,153178,186914,225831,271061,322858,
%U 382038,448869,524451,608914,704204,810459,927883,1057828,1201162
%N Successive sums of consecutive primes that form a triangular grid.
%C 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
%e The consecutive primes 2,3,5,7,11,13 form the triangular grid,
%e ....... 2
%e ..... 3 5
%e ... 7 11 13
%e These consecutive primes add up to 41, the third entry in the table.
%o (PARI) g2(n) = for(j=1,n,y=g(j*(j+1)/2);print1(y",")) g(n) = local(s=0,x);for(x=1,n,s+=prime(x));s
%Y Cf. A078721.
%Y Partial sums of A007468.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, Jan 10 2007
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