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Partial sum of Goldbach numbers A045917.
2

%I #15 Apr 10 2018 08:23:52

%S 0,1,2,3,5,6,8,10,12,14,17,20,23,25,28,30,34,38,40,43,47,50,54,59,63,

%T 66,71,74,78,84,87,92,98,100,105,111,116,121,128,132,137,145,150,154,

%U 163,167,172

%N Partial sum of Goldbach numbers A045917.

%C If the Goldbach conjecture is false then a(n)=a(n+1) for some n.

%D C. Clawson, Mathematical mysteries, Plenum Press 1996, p. 241.

%H Vincenzo Librandi, <a href="/A045919/b045919.txt">Table of n, a(n) for n = 1..300</a>

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%F a(n) = Sum_{k=1..n} Sum_{i=1..k} A010051(i) * A010051(2k-i). - _Wesley Ivan Hurt_, Apr 07 2018

%t Table[Sum[Sum[(PrimePi[2 k - i] - PrimePi[2 k - i - 1]) (PrimePi[i] - PrimePi[i - 1]), {i, k}], {k, n}], {n, 100}] (* _Wesley Ivan Hurt_, Apr 07 2018 *)

%Y Cf. A002375, A045917, A045922.

%K easy,nonn

%O 1,3

%A _Felice Russo_