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%I #16 Nov 06 2023 02:01:53
%S 8,12,15,20,23,24,35,43,44,59,60,71,75,80,84,92,99,104,128,140,147,
%T 148,155,159,200,204,216,231,251,264,288,295,303,332,336,339,344,363,
%U 384,395,420,439,440,451,455,463,467,468,495,528,539,543,560,587,588,608
%N Integers k such that the k-th triangular number is the sum of 2 consecutive primes.
%e 8 is a term: 8*(8+1)/2 = 36 = 17 + 19.
%e 12 is a term: 12*(12+1)/2 = 78 = 37 + 41.
%t With[{upto=10^5},(Sqrt[Select[8ListConvolve[{1,1},Prime[Range[upto]]]+1,IntegerQ[Sqrt[#]]&]]-1)/2] (* _Paolo Xausa_, Nov 05 2023 *)
%o (PARI) lista(nn) = {for (i=1, nn, vsp = 1 + 8 *(prime(i) + prime(i+1)); if (issquare(vsp), v = sqrtint(vsp) - 1; if (v % 2 ==0, print1(v/2, ", "););););} \\ _Michel Marcus_, Jun 02 2013
%Y Cf. A000217, A001043, A000040, A225077.
%K easy,nonn
%O 1,1
%A _Ctibor O. Zizka_, Feb 19 2010
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