OFFSET

0,2

COMMENTS

The sequence is well defined: for n > 0, by the pigeonhole principle, there are necessarily two distinct integers i and j (say with i > j) such that 3^i == 3^j (mod n); the value 3^i - 3^j is a positive multiple of n containing exactly one positive trit and one negative trit, so a(n) <= (3^i - 3^j) / n.

FORMULA

a(n) = 1 iff n belongs to A174658.

EXAMPLE

For n = 5:

- the first multiple of 5 (alongside their balanced ternary expansions) are:

k k*5 bter(k*5) #1 #T

- --- --------- -- --

1 5 1TT 1 2

2 10 101 2 0

3 15 1TT0 1 2

4 20 1T1T 2 2

- negative and positive trits are first balanced for k = 4,

- so a(5) = 4.

PROG

(PARI) a(n) = { for (k=1, oo, my (m=k*n, s=0, d); while (m, m=(m-d=[0, 1, -1][1+m%3])/3; s+=d); if (s==0, return (k))) }

CROSSREFS

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jul 11 2022

STATUS

approved