A300958 Fixed points of A300956.

0, 15, 21, 21141, 21156, 21162, 40095, 40110, 40116, 72171, 72186, 72192, 93312, 93327, 93333, 112266, 112281, 112287, 124659, 124674, 124680, 145800, 145815, 145821, 164754, 164769, 164775, 181521, 181536, 181542, 202662, 202677, 202683, 221616, 221631

Offset: 1

Author

Rémy Sigrist, Mar 17 2018

Keywords

• nonn
• base

Comments

In ternary representation:

- each term has as many 1's as 2's and the set of positions of 1's is the image under A300956 of the set of positions of 2's and vice versa (where the position 0 corresponds to the unit ternary digit),

- the digit at position a(k) of a term is always zero for any k > 0; in particular, as a(1) = 0, all terms are divisible by 3.

To compute a(n):

- consider the sequence of integers k, say f, such that A300956(k) < k,

- the sequence f starts: 2, 9, 10, 11, 17, 18, 19, 20, 23, 24, 25, 26, 19683, ...

- let g(k, t) be defined for k > 0 and t = 0..2 as: g(k, 0) = 0, g(k, 1) = 3^f(k) + 2 * 3^A300956(f(k)), g(k, 2) = 2 * 3^f(k) + 3^A300956(f(k)),

- let Sum_{i = 0..m} t_i * 3^i be the ternary representation of n-1,

- then a(n) = Sum_{i = 0..m} g(i+1, t_i).

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..6561
• Rémy Sigrist, PARI program for A300958

Crossrefs

Cf. A062756, A081603, A300956.

Programs

PARI

See Links section.

Formula

A062756(a(n)) = A081603(a(n)).