A249490 - OEIS

%I #27 Nov 10 2014 06:50:28

%S 2,3,12,28,63,113,208,296,473,657,946,1236,1661,2071,2688,3228,4059,

%T 4811,5898,6858,8209,9433,11116,12572,14637,16395,18872,21046,23935,

%U 26405,29836,32742,36695,40007,44480,48254,53405,57681,63488,68284,74791,80149,87374

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

%C 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:

%C 2

%C 3 5

%C 7 11 13

%C 17 19 23 29

%C 31 37 41 43 47

%C ...

%C 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.

%H George Stagg, <a href="/A249490/b249490.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%p 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

%t 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 *)

%o (MATLAB/Octave)

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

%o for n=1:30

%o   m=0:floor((n-1)/2);

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

%o end

%o a

%o (PARI) a(n) = sum(m=0,(n-1)\2, prime((n-m)*(n-m-1)/2+m+1)); \\ _Michel Marcus_, Nov 04 2014

%Y Cf. A007468, A079824.

%K nonn,easy

%O 1,1

%A _George Stagg_, Oct 30 2014