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

1,1

Links

Table of n, a(n) for n=1..56.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000217, A001043, A000040, A225077.

Sequence in context: A062373 A180690 A194592 * A287373 A031034 A152758

Adjacent sequences: A175129 A175130 A175131 * A175133 A175134 A175135

Keyword

easy,nonn

Author

Ctibor O. Zizka, Feb 19 2010

Status

approved