A355639 a(n) is the least k > 0 such that the balanced ternary expansion of k*n contains as many negative trits as positive trits.
1, 2, 1, 2, 2, 4, 1, 8, 1, 2, 2, 14, 2, 2, 4, 4, 1, 8, 1, 14, 1, 8, 7, 2, 1, 16, 1, 2, 2, 8, 2, 2, 1, 14, 4, 2, 2, 2, 7, 2, 2, 4, 4, 2, 10, 4, 1, 4, 1, 2, 8, 8, 1, 8, 1, 8, 1, 14, 4, 4, 1, 8, 1, 8, 5, 2, 7, 14, 2, 2, 1, 2, 1, 2, 1, 16, 7, 2, 1, 8, 1, 2, 2, 8
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.
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))) }
Formula
a(n) = 1 iff n belongs to A174658.
Comments