A062169 Triangle T(n, k) = k! mod n for n >= 1, 1 <= k <= n.

0, 1, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 4, 0, 1, 2, 0, 0, 0, 0, 1, 2, 6, 3, 1, 6, 0, 1, 2, 6, 0, 0, 0, 0, 0, 1, 2, 6, 6, 3, 0, 0, 0, 0, 1, 2, 6, 4, 0, 0, 0, 0, 0, 0, 1, 2, 6, 2, 10, 5, 2, 5, 1, 10, 0, 1, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 6, 11, 3, 5, 9, 7, 11, 6, 1, 12, 0, 1, 2, 6, 10, 8, 6, 0, 0, 0, 0, 0

Offset: 1

Author

Henry Bottomley, Jun 11 2001

Keywords

• nonn
• tabl

Examples

			a(7,4) = 4! mod 7 = 24 mod 7 = 3. Rows are:
0;
1,0;
1,2,0;
1,2,2,0;
1,2,1,4,0;
1,2,0,0,0,0;
1,2,6,3,1,6,0;
1,2,6,0,0,0,0,0;
1,2,6,6,3,0,0,0,0;
1,2,6,4,0,0,0,0,0,0;
		

Links

• Harry J. Smith, Table of n, a(n) for n=1..1275

Crossrefs

First zero in each row is when k=A002034. Maximum value in each row is A062170. Number of distinct values in each row is A038203. Cf. A000142, A048158, A051127.

Programs

Mathematica

Table[Mod[Range[n]!, n], {n, 1, 15}] // Flatten (* Jean-François Alcover, Oct 25 2013 *)

PARI

{ n=0; for (k=1, 50, for (m=1, k, write("b062169.txt", n++, " ", m!%k)) ) } \\ Harry J. Smith, Aug 02 2009

Extensions

Definition amended by Georg Fischer, Oct 27 2021