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

Author

Tanya Khovanova, Jun 15 2021

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A000217, A014494, A129545.

Programs

Mathematica

Select[Table[n (n + 1)/2, {n, 0, 200}], EvenQ[#] && ! PrimeQ[# + 1] &]
Select[Accumulate[Range[0,300]],EvenQ[#]&&!PrimeQ[#+1]&] (* Harvey P. Dale, Mar 23 2025 *)

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

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