%I
%S 2,4,28,34,47,62,228,256,258,341,848,1362,1709,2262,2692,7907,10396,
%T 10501
%N Numbers k such that k!*T(k)  1 is prime, where T(k) is the kth triangular number.
%C The PFGW program has been used to certify all the terms up to a(18), using a deterministic test which exploits the factorization of a(n) + 1.  _Giovanni Resta_, Jun 24 2018
%H Maheswara Rao Valluri, <a href="https://arxiv.org/abs/1803.11461">Primes of the form p = 1 + n! Sum n, for some n ∈ N*</a>, arXiv:1803.11461 [math.GM], 2018.
%t Do[If[ PrimeQ[n(n +1)!/2  1], Print@ n], {n, 3000}]
%o (PARI) isok(n) = ispseudoprime(n(n+1)!/ 2  1);
%Y Cf. A302859, A301373.
%K nonn,more
%O 1,1
%A _Maheswara Rao Valluri_, Jun 22 2018
%E a(16)a(18) from _Giovanni Resta_, Jun 24 2018
