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A034955
Even triangular numbers with prime indices.
3
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
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
KEYWORD
nonn
AUTHOR
Patrick De Geest, Oct 15 1998
STATUS
approved