A350656 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).

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, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 38, 40, 40, 40, 40, 46, 46, 48, 48, 48, 48, 52, 52, 54, 55, 56, 57, 58, 58, 60, 61, 62, 63, 64, 65, 66, 67

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..67.

Example

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) = min({ 9, 10, 12, 14 }) = 9.

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[Min@ NestWhileList[f, #, UnsameQ, All] &, 68, 0] (* Michael De Vlieger, Jan 15 2022 *)

Prog

(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[1]

Crossrefs

Cf. A065363, A350229, A350657.

Sequence in context: A162906 A378993 A356397 * A100476 A290083 A248517

Adjacent sequences: A350653 A350654 A350655 * A350657 A350658 A350659

Keyword

nonn,base

Author

Rémy Sigrist, Jan 10 2022

Status

approved