This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A301373 #44 Jun 24 2018 08:35:47
%S A301373 1,2,3,4,5,6,7,8,9,10,12,13,14,19,24,251,374,953,1104,1507,3390,4443,
%T A301373 5762
%N A301373 Numbers k such that (k+1)!*k/2 + 1 is prime.
%C A301373 The associated primes are A300559(a(n)) = A180119(a(n))+1 = A001286(a(n)+1)+1. - _M. F. Hasler_, Apr 10 2018
%C A301373 Looking for primes of the form p(n) = 1 + n! f(n) with a simple polynomial function f, it appears that the choice f(n) = n(n+1)/2 = A000217 is one of the most successful choices for getting a maximum of primes for n = 1..20. - _M. F. Hasler_, Apr 14 2018
%C A301373 The PFGW program has been used to certify all the terms up to a(23), using a deterministic test which exploits the factorization of a(n) - 1. - _Giovanni Resta_, Jun 24 2018
%H A301373 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 A301373 Do[ If[ PrimeQ[n(n +1)!/2 +1], Print@ n], {n, 4000}] (* _Robert G. Wilson v_, Apr 05 2018 *)
%o A301373 (PARI) isok(k) = ispseudoprime((k+1)! * k / 2 + 1);
%Y A301373 Cf. A090703, A300559, A180119, A001286.
%Y A301373 See A302859 for the actual primes.
%K A301373 nonn,more
%O A301373 1,2
%A A301373 _Daniel Suteu_, Apr 03 2018
%E A301373 a(21) from _Robert G. Wilson v_, Apr 05 2018
%E A301373 a(22) from _Vaclav Kotesovec_, Apr 06 2018
%E A301373 a(23) from _Giovanni Resta_, Jun 24 2018