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

Author

John W. Layman, May 24 2012

Keywords

• nonn
• base
• look

Comments

The corresponding sequence using binary representations is given in A163381.

Examples

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

Links

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

Crossrefs

Cf. A163381.

Programs

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 *)