A380545 Cumulative sum of the smallest prime in the minimal Goldbach partition for 2*n, n>=2.

2, 5, 8, 11, 16, 19, 22, 27, 30, 33, 38, 41, 46, 53, 56, 59, 64, 71, 74, 79, 82, 85, 90, 93, 98, 105, 108, 113, 120, 123, 126, 131, 138, 141, 146, 149, 152, 157, 164, 167, 172, 175, 180, 187, 190, 195, 202, 221, 224, 229, 232, 235, 240, 243, 246, 251, 254, 259

Offset: 2

Author

Michel Eduardo Beleza Yamagishi, Jun 23 2025

Keywords

• nonn

Examples

			For n = 2, 4 = 2 + 2, the smallest prime p_1 = 2, so a(2) = A020481(2) = 2 = 2.
For n = 3, 6 = 3 + 3, the smallest prime p_2 = 3, so a(3) = a(2) + A020481(3) = 2 + 3 = 5.
For n = 4, 8 = 3 + 5, the smallest prime p_3 = 3, so a(4) = a(3) + A020481(4) = 5 + 3 = 8.
		

Crossrefs

Partial sums of A020481.

Programs

Mathematica

GoldbachMinPrimeCumSum[N_] := If[N < 4, {}, Accumulate[Table[Select[Prime[Range[PrimePi[n]]], PrimeQ[n - #] &, 1][[1]], {n, 4, N, 2}]]]

Formula

a(2) = A020481(2) and a(n) = a(n-1) + A020481(n) for n>2.