A345350 Even triangular numbers such that the next integer is nonprime.

0, 120, 300, 406, 496, 528, 666, 780, 1176, 1378, 1540, 1770, 2278, 2628, 3160, 3240, 3486, 3828, 4186, 4278, 5356, 5460, 5886, 6670, 6786, 7140, 7260, 7626, 7750, 8128, 8256, 9316, 9730, 10296, 10440, 10878, 11476, 11628, 12090, 12246, 12880, 13530, 14706, 15576

Offset

1,2

Comments

Subsequence of A000217 (triangular numbers) and A014494 (even triangular numbers).

Links

Table of n, a(n) for n=1..44.

Example

Even triangular numbers 6, 10, 28, 36, 66, and 78 are all followed by a prime number. Even triangular number 120 is followed by a composite number 121. Thus, a(1) = 120.

Mathematica

Select[Table[n (n + 1)/2, {n, 0, 200}], EvenQ[#] && ! PrimeQ[# + 1] &]

Prog

(Python)
from sympy import isprime
def A014494(n): return (2*n+1)*(2*n+1-(-1)**n)//2
def ok(et): return not isprime(et+1)
print(list(filter(ok, (A014494(n) for n in range(90))))) # Michael S. Branicky, Jun 15 2021
(PARI) lista(nn) = for (n=1, nn, my(t=n*(n+1)/2); if (!(t%2) && !isprime(t+1), print1(t, ", "))) \\ Michel Marcus, Jun 16 2021

Crossrefs

Cf. A000217, A014494, A129545.

Sequence in context: A257712 A250607 A076579 * A121898 A048190 A090391

Adjacent sequences: A345347 A345348 A345349 * A345351 A345352 A345353

Keyword

nonn

Author

Tanya Khovanova, Jun 15 2021

Status

approved