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 A362777 #11 Jun 25 2023 01:02:30 %S A362777 2,3,5,7,13,19,25,49,73,97,121,241,361,481,601,721,1441,2161,2881, %T A362777 3601,4321,5041,10081,15121,20161,25201,30241,35281,40321,80641, %U A362777 120961,161281,201601,241921,282241,322561,362881,725761,1088641,1451521,1814401,2177281,2540161,2903041,3265921 %N A362777 Triangular array read by rows: T(n,k) = n!*k + 1, n >= 1, 1 <= k <= n. %C A362777 These numbers are used in a simple proof of the infinitude of the primes: n!*i + 1 and n!*j + 1 are coprime for 1 <= i < j <= n, so for any n we get n coprime integers (greater than 1) and hence we get at least n distinct primes. %e A362777 Triangle T(n,k) begins: %e A362777 n\k 1 2 3 4 5 6 ... %e A362777 1 2 %e A362777 2 3 5 %e A362777 3 7 13 19 %e A362777 4 25 49 73 97 %e A362777 5 121 241 361 481 601 %e A362777 6 721 1441 2161 2881 3601 4321 %e A362777 ... %Y A362777 Cf. A362778, A362779. %Y A362777 Cf. A038507 (1st column), A188914 (right diagonal). %K A362777 tabl,nonn %O A362777 1,1 %A A362777 _Joe B. Stephen_, May 03 2023