A059835 Form triangle as follows: start with three single digits: 0, 1, 2. Each succeeding row is a concatenation of the previous three rows.

0, 1, 2, 0, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2, 0, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2, 0, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2

Offset: 0

Author

Jason Earls, Feb 25 2001

Keywords

• easy
• nonn
• tabf
• base

Comments

Trajectory of 0 under the morphism 0 -> 1, 1-> 2, 2 -> 012. - Robert G. Wilson v, May 20 2014

The sequence of row lengths is A000213. - Michael Somos, May 22 2014

Examples

			Triangle begins:
  0
  1
  2
  0 1 2
  1 2 0 1 2
  2 0 1 2 1 2 0 1 2
  ...
		

References

• C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, p. 273.

Links

• C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A059832.

Programs

Maple

T:= proc(n) option remember;
      `if`(n<3, n, seq(T(i), i=n-3..n-1))
    end:
seq(T(n), n=0..10);  # Alois P. Heinz, May 22 2014

Mathematica

NestList[ Flatten[# /. {0 -> {1}, 1 -> {2}, 2 -> {0, 1, 2}}] &, {0}, 8] // Flatten (* Robert G. Wilson v, May 20 2014 *)

Formula

a(n) = A059832(n) - 1. - Sean A. Irvine, Oct 11 2022

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Feb 26 2001