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

1,2

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

Formula

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A062756, A081603, A300956.

Sequence in context: A205597 A307792 A236764 * A066758 A338119 A297931

Adjacent sequences: A300955 A300956 A300957 * A300959 A300960 A300961

Keyword

nonn,base

Author

Rémy Sigrist, Mar 17 2018

Status

approved