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

1,3

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

Formula

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

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 *)

Crossrefs

Cf. A002375, A045917, A045922.

Sequence in context: A352077 A213857 A011864 * A224955 A006856 A249013

Adjacent sequences: A045916 A045917 A045918 * A045920 A045921 A045922

Keyword

easy,nonn

Author

Felice Russo

Status

approved