login
A175132
Integers k such that the k-th triangular number is the sum of 2 consecutive primes.
1
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
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
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Feb 19 2010
STATUS
approved