A350656 - OEIS

%I #9 Jan 24 2022 16:11:59

%S 0,1,2,3,4,4,6,7,8,9,10,11,12,13,12,12,16,16,18,19,20,21,22,22,24,25,

%T 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,38,40,40,40,40,46,46,48,

%U 48,48,48,52,52,54,55,56,57,58,58,60,61,62,63,64,65,66,67

%N a(n) is the least value of the orbit of n under repeated application of A350229 (the sum of a number and its balanced ternary digits).

%C The sequence { a(n) - n, n >= 0 } has no lower limit (this because the sequence A065363 can be negative on arbitrarily large intervals).

%e For n = 9:

%e - the orbit of 9 contains the following values:

%e   k  v   bter(v)  ds(v)

%e   -  --  -------  -----

%e   0   9      100      1

%e   1  10      101      2

%e   2  12      110      2

%e   3  14     1TTT     -2

%e   4  12      110      2

%e - so a(9) = min({ 9, 10, 12, 14 }) = 9.

%t 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[Min@ NestWhileList[f, #, UnsameQ, All] &, 68, 0] (* _Michael De Vlieger_, Jan 15 2022 *)

%o (PARI) b(n) = my (v=n, d); while (n, n=(n-d=[0,1,-1][1+n%3])/3; v+=d); v

%o a(n) = my (s=[]); while (!setsearch(s, n), s=setunion(s, [n]); n=b(n)); s[1]

%Y Cf. A065363, A350229, A350657.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Jan 10 2022