A129545 Triangular numbers T such that T+1 is a prime.

1, 6, 10, 28, 36, 66, 78, 136, 190, 210, 276, 378, 630, 820, 946, 990, 1128, 1326, 1596, 1830, 2016, 2080, 2346, 2556, 2850, 2926, 3570, 3916, 4560, 4656, 4950, 5050, 5778, 6216, 6328, 8646, 8778, 9180, 9870, 11026, 12720, 13366, 14028, 14196, 14878

Offset: 1

Author

Zak Seidov, May 30 2007

Keywords

• nonn
• easy

Comments

The only triangular numbers T such that T-1 is a (positive) prime are 3 and 6.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A055469, A129755, A130178, A345350.

Programs

Mathematica

Select[Accumulate[Range[200]],PrimeQ[#+1]&] (* Harvey P. Dale, Nov 08 2011 *)

Python

from sympy import isprime
def T(n): return n*(n+1)//2
def ok(T): return isprime(T+1)
print(list(filter(ok, (T(n) for n in range(175))))) # Michael S. Branicky, Jun 18 2021

Formula

a(n) = A000217(A067186(n)). - R. J. Mathar, Dec 10 2007

a(n) = A055469(n) - 1. - Joerg Arndt, Jun 19 2021