A300956 a(0) = 0, a(1) = 2, a(2) = 1, and for any n > 2 with ternary representation n = Sum_{i=0..k} t_i * 3^i, a(n) = Sum_{i=0..k} a(t_i) * 3^a(i).

0, 2, 1, 18, 20, 19, 9, 11, 10, 6, 8, 7, 24, 26, 25, 15, 17, 16, 3, 5, 4, 21, 23, 22, 12, 14, 13, 774840978, 774840980, 774840979, 774840996, 774840998, 774840997, 774840987, 774840989, 774840988, 774840984, 774840986, 774840985, 774841002, 774841004

Offset: 0

Author

Rémy Sigrist, Mar 17 2018

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the natural numbers.

This sequence has connections with A300955.

This sequence has infinitely many fixed points (A300958); for any k >= 0, at least one of k or 3^k + 2 * 3^a(k) is a fixed point.

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A160384, A300955, A300958 (fixed points).

Programs

PARI

a(n) = my (t=Vecrev(digits(n,3))); sum(i=0, #t-1, if (t[i+1]==1, 2, t[i+1]==2, 1, 0) * 3 ^ a(i))

Formula

A160384(a(n)) = A160384(n).

a(a(n)) = n.