login
A129545
Triangular numbers T such that T+1 is a prime.
6
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
1,2
COMMENTS
The only triangular numbers T such that T-1 is a (positive) prime are 3 and 6.
LINKS
FORMULA
a(n) = A000217(A067186(n)). - R. J. Mathar, Dec 10 2007
a(n) = A055469(n) - 1. - Joerg Arndt, Jun 19 2021
MATHEMATICA
Select[Accumulate[Range[200]], PrimeQ[#+1]&] (* Harvey P. Dale, Nov 08 2011 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, May 30 2007
STATUS
approved