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

%I A380545 #38 Jun 24 2025 15:14:30
%S A380545 2,5,8,11,16,19,22,27,30,33,38,41,46,53,56,59,64,71,74,79,82,85,90,93,
%T A380545 98,105,108,113,120,123,126,131,138,141,146,149,152,157,164,167,172,
%U A380545 175,180,187,190,195,202,221,224,229,232,235,240,243,246,251,254,259
%N A380545 Cumulative sum of the smallest prime in the minimal Goldbach partition for 2*n, n>=2.
%F A380545 a(2) = A020481(2) and a(n) = a(n-1) + A020481(n) for n>2.
%e A380545 For n = 2, 4 = 2 + 2, the smallest prime p_1 = 2, so a(2) = A020481(2) = 2 = 2.
%e A380545 For n = 3, 6 = 3 + 3, the smallest prime p_2 = 3, so a(3) = a(2) + A020481(3) = 2 + 3 = 5.
%e A380545 For n = 4, 8 = 3 + 5, the smallest prime p_3 = 3, so a(4) = a(3) + A020481(4) = 5 + 3 = 8.
%t A380545 GoldbachMinPrimeCumSum[N_] := If[N < 4, {}, Accumulate[Table[Select[Prime[Range[PrimePi[n]]], PrimeQ[n - #] &, 1][[1]], {n, 4, N, 2}]]]
%Y A380545 Partial sums of A020481.
%K A380545 nonn
%O A380545 2,1
%A A380545 _Michel Eduardo Beleza Yamagishi_, Jun 23 2025