A362777 - OEIS

%I #11 Jun 25 2023 01:02:30

%S 2,3,5,7,13,19,25,49,73,97,121,241,361,481,601,721,1441,2161,2881,

%T 3601,4321,5041,10081,15121,20161,25201,30241,35281,40321,80641,

%U 120961,161281,201601,241921,282241,322561,362881,725761,1088641,1451521,1814401,2177281,2540161,2903041,3265921

%N Triangular array read by rows: T(n,k) = n!*k + 1, n >= 1, 1 <= k <= n.

%C 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 Triangle T(n,k) begins:

%e   n\k  1    2    3    4    5    6 ...

%e   1    2

%e   2    3    5

%e   3    7   13   19

%e   4   25   49   73   97

%e   5  121  241  361  481  601

%e   6  721 1441 2161 2881 3601 4321

%e   ...

%Y Cf. A362778, A362779.

%Y Cf. A038507 (1st column), A188914 (right diagonal).

%K tabl,nonn

%O 1,1

%A _Joe B. Stephen_, May 03 2023