A175132 Integers k such that the k-th triangular number is the sum of 2 consecutive primes.

8, 12, 15, 20, 23, 24, 35, 43, 44, 59, 60, 71, 75, 80, 84, 92, 99, 104, 128, 140, 147, 148, 155, 159, 200, 204, 216, 231, 251, 264, 288, 295, 303, 332, 336, 339, 344, 363, 384, 395, 420, 439, 440, 451, 455, 463, 467, 468, 495, 528, 539, 543, 560, 587, 588, 608

Offset: 1

Author

Ctibor O. Zizka, Feb 19 2010

Keywords

• easy
• nonn

Examples

			8 is a term: 8*(8+1)/2 = 36 = 17 + 19.
12 is a term: 12*(12+1)/2 = 78 = 37 + 41.
		

Crossrefs

Cf. A000217, A001043, A000040, A225077.

Programs

Mathematica

With[{upto=10^5},(Sqrt[Select[8ListConvolve[{1,1},Prime[Range[upto]]]+1,IntegerQ[Sqrt[#]]&]]-1)/2] (* Paolo Xausa, Nov 05 2023 *)

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