A071154 Totally balanced decimal numbers: if we assign the weight w(d) = d-1 to each digit d (i.e., w(0) = -1, w(1) = 0, ..., w(9) = 8) and then read the digits of the term from left to right, the partial sum of the weights is never negative and the total weighted sum is zero.

1, 11, 20, 111, 120, 201, 210, 300, 1111, 1120, 1201, 1210, 1300, 2011, 2020, 2101, 2110, 2200, 3001, 3010, 3100, 4000, 11111, 11120, 11201, 11210, 11300, 12011, 12020, 12101, 12110, 12200, 13001, 13010, 13100, 14000, 20111, 20120, 20201

Offset: 1

Author

Antti Karttunen, May 14 2002

Keywords

• nonn
• base

Comments

The initial portion of this sequence (up to the 6917th term) is equal to A071153 (Łukasiewicz words for rooted plane trees) sorted in ascending order.

Links

• OEIS Wiki, Łukasiewicz words
• Index entries for sequences related to Łukasiewicz

Crossrefs

Subset of A061384. Superset of A071161.

Cf. A014486 (totally balanced binary numbers), A071153.

Programs

PARI

isok(n) = {my(s = 0); my(d = digits(n)); for (k=1, #d, s += d[k]-1; if (s<0, return (0));); if (s, 0, 1);} \\ Michel Marcus, Oct 16 2015