A207339 Triangular numbers T from A000217 such that (4*T+1)/5 is prime.

6, 21, 36, 66, 91, 136, 171, 351, 496, 561, 741, 946, 1176, 1326, 1596, 2016, 2346, 2701, 2926, 3321, 3486, 4851, 6216, 6441, 7626, 8646, 8911, 9591, 10011, 10296, 11026, 11476, 13041, 15051, 16471, 16836, 17391, 18336, 19701, 21736

Offset: 1

Author

Wolfdieter Lang, Feb 27 2012

Keywords

• nonn

Comments

The corresponding primes are gven in A207337, where also equivalent formulations are found.

The indices of these triangular numbers are given by (A002733(n)-1)/2.

Examples

			a(3) = 36 = T((17-1)/2) = T(8)=A000217(8). (4*36+1)/5 = 29 = A207337(3).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A207337, A129307, A027862, A002731.

Programs

Mathematica

Select[Accumulate[Range[300]],PrimeQ[(4#+1)/5]&] (* Harvey P. Dale, Sep 18 2019 *)

Formula

a(n) = T(K(n)):= A000217(K(n)) with K(n)=(m(n)-1)/2, and m(n) given in A002733(n).