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

Author

Rémy Sigrist, Jul 11 2022

Keywords

• nonn
• base

Comments

A174658 corresponds to fixed points.

Examples

			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.
		

Crossrefs

See A143146 for a similar sequence.

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

Programs

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))) }

Formula

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