A208294 Triangular numbers T from A000217 such that (4*T+1)/13 is prime.

55, 120, 1485, 1953, 2278, 2850, 3240, 6555, 9870, 10585, 16110, 17020, 18528, 34453, 36585, 37950, 47895, 49455, 52003, 56280, 57970, 70125, 72010, 80200, 96580, 110685, 127260, 129795, 133903, 165025, 169653, 172578, 244650

Offset: 1

Author

Wolfdieter Lang, Feb 27 2012

Keywords

• nonn

Comments

The corresponding primes are gven in A208292, where equivalent formulations are found.

The indices of these triangular numbers are given by (A208293(n)-1)/2.

Examples

			a(2) = 120. m(2)= 31: 120 = T((31-1)/2) = T(15)=A000217(15). (4*120+1)/13 = 37 = A208292(2).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A208292. A208293, A207337, A207339, A129307, A027862, A002731.

Programs

Mathematica

tri = # (# + 1)/2 & /@ Range@ 1000; Select[ tri, PrimeQ[(4 # + 1)/13] &] (* Robert G. Wilson v, Feb 28 2012 *)

Formula

a(n) = T(K(n)):= A000217(K(n)) with K(n)=(A208293(n)-1)/2.