cp's OEIS Frontend

A163380 a(n) = the (decimal equivalent of the) largest integer that can be made by rotating the binary digits of n any number of positions to the left or right.

%I A163380 #20 Sep 24 2017 02:31:38
%S A163380 1,2,3,4,6,6,7,8,12,10,14,12,14,14,15,16,24,20,28,20,26,26,30,24,28,
%T A163380 26,30,28,30,30,31,32,48,40,56,36,50,52,60,40,52,42,58,50,54,58,62,48,
%U A163380 56,50,60,52,58,54,62,56,60,58,62,60,62,62,63,64,96,80,112,72,98,104,120
%N A163380 a(n) = the (decimal equivalent of the) largest integer that can be made by rotating the binary digits of n any number of positions to the left or right.
%C A163380 By rotating the binary digits of n, it is meant: Write n in binary without any leading 0's. To rotate this string to the right, say, by one position, first remove the rightmost digit and then append it on the left side of the remaining string. (So the least significant digit becomes the most significant digit.) Here, leading 0's are not removed after the first rotation, so that each binary string being rotated has the same number of binary digits as n has.
%H A163380 Alois P. Heinz, <a href="/A163380/b163380.txt">Table of n, a(n) for n = 1..8192</a>
%e A163380 13 in binary is 1101. Rotating this just once to the right, we get 1110, 14 in decimal. If we rotate twice to the right, we would have had 0111 = 7 in decimal. Rotating 3 times, we end up with 1011, which is 11 in decimal. Rotating 4 times, we end up at the beginning with 1101 = 13. 14 is the largest of these, so a(13) = 14.
%p A163380 rot := proc(n,t) convert(n,base,2) ; bdgs := ListTools[Rotate](%,t) ; add(op(i,bdgs)*2^(i-1),i=1..nops(bdgs)) ; end: A163380 := proc(n) local a,r; a := n ; for r from 1 to ilog2(n) do a := max(a, rot(n,r)) ; od: a; end: seq(A163380(n),n=1..100) ; # _R. J. Mathar_, Aug 03 2009
%t A163380 Table[With[{d = IntegerDigits[n, 2]}, Max@ Map[FromDigits[#, 2] &@ RotateRight[d, #] &, Range[Length@ d]]], {n, 71}] (* _Michael De Vlieger_, Sep 23 2017 *)
%Y A163380 Cf. A163381, A163382, A256999.
%K A163380 base,nonn,look
%O A163380 1,2
%A A163380 _Leroy Quet_, Jul 25 2009
%E A163380 More terms from _R. J. Mathar_, Aug 03 2009