A249490 a(n) = Sum_{m=0..floor((n-1)/2)} prime((n-m)(n-m-1)/2+m+1).

2, 3, 12, 28, 63, 113, 208, 296, 473, 657, 946, 1236, 1661, 2071, 2688, 3228, 4059, 4811, 5898, 6858, 8209, 9433, 11116, 12572, 14637, 16395, 18872, 21046, 23935, 26405, 29836, 32742, 36695, 40007, 44480, 48254, 53405, 57681, 63488, 68284, 74791, 80149, 87374

Offset: 1

Author

George Stagg, Oct 30 2014

Keywords

• nonn
• easy

Comments

Arrange the prime numbers into a triangle, with 2 at the top, 3 and 5 in the second row, 7, 11 and 13 in the third row, and so on:

2

3 5

7 11 13

17 19 23 29

31 37 41 43 47

...

The n-th term in the sequence is then the sum of the numbers in the upward diagonal beginning on the n-th row of this triangle.

Examples

			a(1) = 2; a(2) = 3; a(3) = 7+5 = 12; a(4) = 17+11 = 28.
		

Links

• George Stagg, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007468, A079824.

Programs

Maple

A249490:=n->add(ithprime((n-m)*(n-m-1)/2+m+1), m=0..floor((n-1)/2)): seq(A249490(n), n=1..50); # Wesley Ivan Hurt, Nov 07 2014

Mathematica

Table[Sum[Prime[(n - m) (n - m - 1)/2 + m + 1], {m, 0, Floor[(n - 1)/2]}], {n, 50}] (* Wesley Ivan Hurt, Nov 07 2014 *)

PARI

a(n) = sum(m=0,(n-1)\2, prime((n-m)*(n-m-1)/2+m+1)); \\ Michel Marcus, Nov 04 2014

Formula

a(n) = Sum_{m=0..floor((n-1)/2)} prime((n-m)(n-m-1)/2+m+1).