A084348 Triangle read by rows: T(n,k) = floor(e*k!) - n*floor(e*k!/n).

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

Offset

1,4

Comments

Original name: Triangle in which row n gives periodic part of a certain map.

Let r(k,n) = floor(e*k!)-n*floor(e*k!/n) then for any n integer>0, sequence r(k,n) is n-periodic. Sequence gives periods of r(k,n) for fixed n.

Links

Table of n, a(n) for n=1..102.

Example

If n=7, r(k,7) is sequence 2, 5, 2, 2, 4, 4, 1, 2, 5, 2, 2, 4, 4, 1, 2, 5, 2, 2, 4, 4, 1, 2, 5, 2, 2, 4, 4, 1, 2, 5...... 7-periodic with period: (2, 5, 2, 2, 4, 4, 1).
Triangle begins:
  0;
  0, 1;
  2, 2, 1;
  2, 1, 0, 1;
  2, 0, 1, 0, 1;
  2, 5, 4, 5, 2, 1;
  2, 5, 2, 2, 4, 4, 1;
  ...

Crossrefs

Cf. A084351.

Sequence in context: A038540 A335060 A333058 * A210580 A284478 A298948

Adjacent sequences: A084345 A084346 A084347 * A084349 A084350 A084351

Keyword

nonn,tabl

Author

Benoit Cloitre, Jun 22 2003

Extensions

Name changed by Sean A. Irvine, Mar 30 2026

Status

approved