A206803 Sum_{0A065091(j) is the j-th odd prime.

2, 8, 26, 52, 98, 156, 242, 376, 528, 740, 996, 1276, 1608, 2024, 2530, 3068, 3708, 4420, 5170, 6040, 6994, 8080, 9350, 10716, 12132, 13652, 15226, 16912, 19004, 21216, 23614, 26076, 28868, 31728, 34798, 38084, 41518, 45180, 49076

Offset: 2

Author

Clark Kimberling, Feb 13 2012

Keywords

• nonn

Comments

Partial sums of A185382.

Links

• Danny Rorabaugh, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A065091, A185382, A206804, A206817.

Programs

Mathematica

s[k_] := Prime[k + 1]; t[1] = 0;
p[n_] := Sum[s[k], {k, 1, n}];
c[n_] := n*s[n] - p[n]
t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1]
Table[c[n], {n, 2, 100}]  (* A185382 *)
%/2  (* A206802 *)
Flatten[Table[t[n], {n, 2, 40}]]  (*  A206803 *)
%/2  (* A206804 *)

Sage

[sum([sum([nth_prime(k+1)-nth_prime(j+1) for j in range(1,k)]) for k in range(2,n+1)]) for n in range(2,41)] # Danny Rorabaugh, Apr 18 2015