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

1,1

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000217, A002145.

Cf. A014493, A034953, A034954.

Sequence in context: A033588 A014635 A227970 * A117978 A119174 A326134

Adjacent sequences: A034952 A034953 A034954 * A034956 A034957 A034958

Keyword

nonn

Author

Patrick De Geest, Oct 15 1998

Status

approved