A350657 a(n) is the greatest value of the orbit of n under repeated application of A350229 (the sum of a number and its balanced ternary digits).
0, 2, 2, 6, 6, 6, 6, 8, 8, 14, 14, 14, 14, 16, 14, 15, 16, 17, 18, 20, 20, 24, 24, 24, 24, 26, 26, 32, 32, 32, 32, 44, 32, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 46, 47, 48, 50, 50, 51, 52, 53, 54, 56, 56, 60, 60, 60, 60, 62, 62, 68, 68, 68, 68
Offset: 0
Examples
For n = 9:
- the orbit of 9 contains the following values:
k v bter(v) ds(v)
- -- ------- -----
0 9 100 1
1 10 101 2
2 12 110 2
3 14 1TTT -2
4 12 110 2
- so a(9) = max({ 9, 10, 12, 14 }) = 14.
Programs
-
Mathematica
f[n_] := n + Total[If[First@ # == 0, Rest@ #, #] &[Prepend[IntegerDigits[n, 3], 0] //. {x___, y_, k_ /; k > 1, z___} :> {x, y + 1, k - 3, z}]]; Array[Max@ NestWhileList[f, #, UnsameQ, All] &, 67, 0] (* Michael De Vlieger, Jan 15 2022 *) -
PARI
b(n) = my (v=n, d); while (n, n=(n-d=[0,1,-1][1+n%3])/3; v+=d); v a(n) = my (s=[]); while (!setsearch(s, n), s=setunion(s, [n]); n=b(n)); s[#s]
Comments