A034955 Even triangular numbers with prime indices.

6, 28, 66, 190, 276, 496, 946, 1128, 1770, 2278, 2556, 3160, 3486, 5356, 5778, 8128, 8646, 9730, 11476, 13366, 14028, 16110, 18336, 19900, 22366, 24976, 25878, 28680, 31626, 34716, 36856, 40186, 47278, 48516, 54946, 60378, 64620, 67528, 72010, 73536, 87990

Offset: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn

Comments

For prime indices p such that p(p+1)/2 is even, see A002145 (Primes of form 4n+3).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Eric Weisstein's World of Mathematics, Triangular Number

Crossrefs

Cf. A000217, A002145.

Cf. A014493, A034953, A034954.

Programs

Mathematica

Select[Table[Prime[n] (Prime[n] + 1)/2, {n, 500}], EvenQ[#] &] (* G. C. Greubel, Nov 03 2017 *)

Python

from sympy import primerange
def aupto(lim):
    pitri = (p*(p+1)//2 for p in primerange(2, int((2*lim)**.5)+1))
    return [t for t in pitri if t%2 == 0]
print(aupto(90000)) # Michael S. Branicky, Jun 28 2021

Formula

a(n) = A000217(A002145(n)). - Michel Marcus, Nov 04 2017