A045919 Partial sum of Goldbach numbers A045917.

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, 66, 71, 74, 78, 84, 87, 92, 98, 100, 105, 111, 116, 121, 128, 132, 137, 145, 150, 154, 163, 167, 172

Offset: 1

Author

Felice Russo

Keywords

• easy
• nonn

Comments

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

References

• C. Clawson, Mathematical mysteries, Plenum Press 1996, p. 241.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..300
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A002375, A045917, A045922.

Programs

Mathematica

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 *)

Formula

a(n) = Sum_{k=1..n} Sum_{i=1..k} A010051(i) * A010051(2k-i). - Wesley Ivan Hurt, Apr 07 2018