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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.

%I A212713 #16 Jan 29 2025 15:59:27
%S A212713 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,
%T A212713 13,16,11,22,25,4,13,22,13,40,41,14,41,44,5,14,23,16,41,50,17,44,53,2,
%U A212713 5,8,11,14,17,20,23,26,7,16,25,22,41,44,23,50,53,8
%N 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.
%C A212713 The corresponding sequence using binary representations is given in A163381.
%H A212713 Alois P. Heinz, <a href="/A212713/b212713.txt">Table of n, a(n) for n = 1..6559</a>
%e A212713 For n=10, the rotations are 101(base 3)=10, 011=4, and 110=12, so a(10)=4.
%p A212713 a:= proc(n) local i, k, m, s;
%p A212713       k, m, s:= ilog[3](n), n, n;
%p A212713       for i to k do m:= iquo(m, 3, 'd') +d*3^k; s:=s, m od;
%p A212713       min(s)
%p A212713     end:
%p A212713 seq(a(n), n=1..80);  # _Alois P. Heinz_, May 24 2012
%t A212713 a = {}; For[n = 1, n <= 100, n++, {m = n; d = IntegerDigits[n, 3];
%t A212713   For[k = 1, k <= Length[d], k++, {d = RotateLeft[d]; v = FromDigits[d, 3]; If[v < m, m = v]; }]; AppendTo[a, m]}]; a
%t A212713 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 *)
%Y A212713 Cf. A163381.
%K A212713 nonn,base,look
%O A212713 1,2
%A A212713 _John W. Layman_, May 24 2012