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 A111392 #15 Dec 06 2018 03:43:36
%S A111392 2,5,187,162319,10697595389,63619487169453143,
%T A111392 74365399061678006800073593,11864736003419293844093922527852416537,
%U A111392 601642845102734414280661105098046392912578705726003
%N A111392 a(n) = Product_{i=1..n-1} (Product_{k=1..i} p_k + Product_{k=i+1..n} p_k).
%C A111392 This sequence gives another proof that there are infinitely many primes. Let N = Product_{1<=i<n} (Product_{1<=k<=i} p_k + Product_{i<k<=n} p_k). Suppose there are only a finite number of primes p_i, 1<=i<=n. If N is prime, then for all i, not(N=p_i). Because, for all i, p_i<N. If N is composite, then it must have a prime divisor p which is different from primes p_i. Because, for all i, not(N==0 mod p_i).
%C A111392 a(1) could also be chosen to be 1.
%H A111392 Vincenzo Librandi, <a href="/A111392/b111392.txt">Table of n, a(n) for n = 1..29</a>
%p A111392 a:=n->mul(mul(ithprime(k),k=1..i)+mul(ithprime(k),k=i+1..n),i=1..n-1): 2,seq(a(n),n=2..10); # _Muniru A Asiru_, Dec 06 2018
%t A111392 Join[{2}, Rest[f[n_]:=Product[(Product[Prime[k], {k, i}] + Product[Prime[k], {k, i + 1, n}]), {i, n - 1}]; Array[f, 10] ]] (* _Robert G. Wilson v_, Nov 12 2005 *)
%o A111392 (PARI) t=10; for(n=2, t, print1(prod(i=1, n-1, prod(k=1,i,prime(k)) + prod(k=i+1,n,prime(k))), ", ")); \\ _Gerald McGarvey_, Nov 12 2005
%Y A111392 Cf. A024451, A112404.
%K A111392 nonn,nice
%O A111392 1,1
%A A111392 _Yasutoshi Kohmoto_, Nov 08 2005
%E A111392 Corrected and extended by _Gerald McGarvey_ and _Robert G. Wilson v_, Nov 12 2005