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%I #21 Feb 22 2022 19:27:31
%S 1,6,10,28,36,66,78,136,190,210,276,378,630,820,946,990,1128,1326,
%T 1596,1830,2016,2080,2346,2556,2850,2926,3570,3916,4560,4656,4950,
%U 5050,5778,6216,6328,8646,8778,9180,9870,11026,12720,13366,14028,14196,14878
%N Triangular numbers T such that T+1 is a prime.
%C The only triangular numbers T such that T-1 is a (positive) prime are 3 and 6.
%H Harvey P. Dale, <a href="/A129545/b129545.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000217(A067186(n)). - _R. J. Mathar_, Dec 10 2007
%F a(n) = A055469(n) - 1. - _Joerg Arndt_, Jun 19 2021
%t Select[Accumulate[Range[200]],PrimeQ[#+1]&] (* _Harvey P. Dale_, Nov 08 2011 *)
%o (Python)
%o from sympy import isprime
%o def T(n): return n*(n+1)//2
%o def ok(T): return isprime(T+1)
%o print(list(filter(ok, (T(n) for n in range(175))))) # _Michael S. Branicky_, Jun 18 2021
%Y Cf. A000217, A055469, A129755, A130178, A345350.
%K nonn,easy
%O 1,2
%A _Zak Seidov_, May 30 2007