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

%I A249490 #27 Nov 10 2014 06:50:28
%S A249490 2,3,12,28,63,113,208,296,473,657,946,1236,1661,2071,2688,3228,4059,
%T A249490 4811,5898,6858,8209,9433,11116,12572,14637,16395,18872,21046,23935,
%U A249490 26405,29836,32742,36695,40007,44480,48254,53405,57681,63488,68284,74791,80149,87374
%N A249490 a(n) = Sum_{m=0..floor((n-1)/2)} prime((n-m)(n-m-1)/2+m+1).
%C A249490 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 A249490 2
%C A249490 3 5
%C A249490 7 11 13
%C A249490 17 19 23 29
%C A249490 31 37 41 43 47
%C A249490 ...
%C A249490 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 A249490 George Stagg, <a href="/A249490/b249490.txt">Table of n, a(n) for n = 1..1000</a>
%F A249490 a(n) = Sum_{m=0..floor((n-1)/2)} prime((n-m)(n-m-1)/2+m+1).
%e A249490 a(1) = 2; a(2) = 3; a(3) = 7+5 = 12; a(4) = 17+11 = 28.
%p A249490 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 A249490 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 A249490 (MATLAB/Octave)
%o A249490 p=primes(10000);a=[];
%o A249490 for n=1:30
%o A249490   m=0:floor((n-1)/2);
%o A249490   a=[a,sum(p((n-m).*(n-m-1)./2 + m + 1))];
%o A249490 end
%o A249490 a
%o A249490 (PARI) a(n) = sum(m=0,(n-1)\2, prime((n-m)*(n-m-1)/2+m+1)); \\ _Michel Marcus_, Nov 04 2014
%Y A249490 Cf. A007468, A079824.
%K A249490 nonn,easy
%O A249490 1,1
%A A249490 _George Stagg_, Oct 30 2014