A362778 Triangular array read by rows: T(n,k) is the least prime factor of n!*k + 1, n >= 1, 1 <= k <= n.

2, 3, 5, 7, 13, 19, 5, 7, 73, 97, 11, 241, 19, 13, 601, 7, 11, 2161, 43, 13, 29, 71, 17, 15121, 20161, 11, 30241, 35281, 61, 11, 73, 161281, 449, 241921, 282241, 47, 19, 293, 1088641, 1451521, 23, 2177281, 13, 2903041, 17, 11, 13, 10886401, 233, 18144001, 17, 101, 29030401, 32659201, 43

Offset: 1

Author

Joe B. Stephen, May 03 2023

Keywords

• tabl
• nonn

Comments

The primes in each row are distinct because n!*k + 1 are coprime for 1 <= k <= n, and hence this array gives a simple proof that there are infinitely many prime numbers.

Examples

			Triangle T(n,k) begins:
  n\k  1    2    3    4    5    6 ...
  1    2
  2    3    5
  3    7   13   19
  4    5    7   73   97
  5   11  241   19   13  601
  6    7   11 2161   43   13   29
  ...
		

Crossrefs

Cf. A362777, A362779.

Cf. A051301 (1st column).

Formula

T(n,k) = A020639(A362777(n,k)).