A212713 The (decimal equivalent of the) smallest integer that can be made by rotating the base three digits of n any number of positions to the left or right.

1, 2, 1, 4, 5, 2, 5, 8, 1, 4, 7, 4, 13, 14, 5, 14, 17, 2, 5, 8, 7, 14, 17, 8, 17, 26, 1, 4, 7, 10, 13, 16, 11, 22, 25, 4, 13, 22, 13, 40, 41, 14, 41, 44, 5, 14, 23, 16, 41, 50, 17, 44, 53, 2, 5, 8, 11, 14, 17, 20, 23, 26, 7, 16, 25, 22, 41, 44, 23, 50, 53, 8

Offset

1,2

Comments

The corresponding sequence using binary representations is given in A163381.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..6559

Example

For n=10, the rotations are 101(base 3)=10, 011=4, and 110=12, so a(10)=4.

Maple

a:= proc(n) local i, k, m, s;
      k, m, s:= ilog[3](n), n, n;
      for i to k do m:= iquo(m, 3, 'd') +d*3^k; s:=s, m od;
      min(s)
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, May 24 2012

Mathematica

a = {}; For[n = 1, n <= 100, n++, {m = n; d = IntegerDigits[n, 3];
  For[k = 1, k <= Length[d], k++, {d = RotateLeft[d]; v = FromDigits[d, 3]; If[v < m, m = v]; }]; AppendTo[a, m]}]; a
smr3[n_]:=With[{id3=IntegerDigits[n, 3]}, Min[FromDigits[#, 3]&/@Table[RotateRight[id3, k], {k, Length[id3]}]]]; Array[smr3, 80] (* Harvey P. Dale, Jan 29 2025 *)

Crossrefs

Cf. A163381.

Sequence in context: A359058 A191379 A038574 * A072014 A213526 A308364

Adjacent sequences: A212710 A212711 A212712 * A212714 A212715 A212716

Keyword

nonn,base,look

Author

John W. Layman, May 24 2012

Status

approved