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 A125130 Successive sums of consecutive primes that form a triangular grid. 0

%I

%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.

%K easy,nonn

%O 1,1

%A Cino Hilliard (hillcino368(AT)hotmail.com), Jan 10 2007

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