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
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.
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).
Comments