A102818 Irregular array a(m,k) = A001035(k) mod m read by rows, 1<=k<=16, 3<=m.

1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 4, 4, 1, 3, 4, 4, 1, 3, 4, 4, 1, 3, 4, 4, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 5, 2, 3, 5, 1, 3, 5, 2, 3, 5, 1, 3, 5, 2, 1, 3, 3, 3, 7, 7, 3, 3, 7, 7, 3, 3, 7, 7, 3, 3, 1, 3, 1, 3, 1, 0, 4, 3, 1

Offset: 3

Author

Gerald McGarvey, Feb 26 2005

Keywords

• nonn
• tabf

Comments

Conjectures (based on mod values up to n=99): the sequence A001035(m) is (pre)periodic modulo n for all n, the lengths of the ending periods mod n (except n=4) being given by A011773 (which is related to Carmichael's lambda function).

Examples

			The array starts in row m=3 as:
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0;
1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3;
1 3 4 4 1 3 4 4 1 3 4 4 1 3 4 4;
1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3;
1 3 5 2 3 5 1 3 5 2 3 5 1 3 5 2;
1 3 3 3 7 7 3 3 7 7 3 3 7 7 3 3;
1 3 1 3 1 0 4 3 1 3 1 0 4 3 1 3;
1 3 9 9 1 3 9 9 1 3 9 9 1 3 9 9;
1 3 8 10 7 3 10 10 1 6 1 3 8 10 7 3;
1 3 7 3 7 3 7 3 7 3 7 3 7 3 7 3;
		

Links

• Eric Weisstein's World of Mathematics, Carmichael Function

Crossrefs

Cf. A001035, A011773, A002322.

Programs

Mathematica

seq = List[1, 3, 19, 219, 4231, 130023, 6129859, 431723379, 44511042511, 6611065248783, 1396281677105899, 414864951055853499, 171850728381587059351, 98484324257128207032183, 77567171020440688353049939, 83480529785490157813844256579] Table[Mod[seq, i], {i, 3, 9}]