A355640 a(0) = 0, and for any n > 0, a(n) is the least positive multiple of n whose balanced ternary expansion contains as many negative trits as positive trits.

0, 2, 2, 6, 8, 20, 6, 56, 8, 18, 20, 154, 24, 26, 56, 60, 16, 136, 18, 266, 20, 168, 154, 46, 24, 400, 26, 54, 56, 232, 60, 62, 32, 462, 136, 70, 72, 74, 266, 78, 80, 164, 168, 86, 440, 180, 46, 188, 48, 98, 400, 408, 52, 424, 54, 440, 56, 798, 232, 236, 60

Offset

0,2

Comments

A174658 corresponds to fixed points.

Links

Table of n, a(n) for n=0..60.

Formula

a(n) = n * A355639(n).

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*5 = 20.

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*n))) }

Crossrefs

See A143146 for a similar sequence.

Cf. A065363, A174658 (fixed points), A355639.

Sequence in context: A322132 A054153 A000673 * A370586 A276425 A129383

Adjacent sequences: A355637 A355638 A355639 * A355641 A355642 A355643

Keyword

nonn,base

Author

Rémy Sigrist, Jul 11 2022

Status

approved