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A249490 a(n) = Sum_{m=0..floor((n-1)/2)} prime((n-m)(n-m-1)/2+m+1). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

PROG

(MATLAB/Octave)

p=primes(10000); a=[];

for n=1:30

  m=0:floor((n-1)/2);

  a=[a, sum(p((n-m).*(n-m-1)./2 + m + 1))];

end

a

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

CROSSREFS

Cf. A007468, A079824.

Sequence in context: A016021 A173669 A136703 * A075269 A215602 A325628

Adjacent sequences:  A249487 A249488 A249489 * A249491 A249492 A249493

KEYWORD

nonn,easy

AUTHOR

George Stagg, Oct 30 2014

STATUS

approved

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Last modified July 31 08:50 EDT 2021. Contains 346369 sequences. (Running on oeis4.)