A206803 - OEIS

A206803

Sum_{0<j<k<=n} P(k)-P(j), where P(j)=A065091(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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

COMMENTS

Partial sums of A185382.

LINKS

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

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 *)

PROG

(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

CROSSREFS

Cf. A065091, A185382, A206804, A206817.

Sequence in context: A195585 A102942 A212691 * A212527 A227015 A216929

Adjacent sequences: A206800 A206801 A206802 * A206804 A206805 A206806

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 13 2012

STATUS

approved