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.

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, 26, 30, 28, 30, 30, 31, 32, 48, 40, 56, 36, 50, 52, 60, 40, 52, 42, 58, 50, 54, 58, 62, 48, 56, 50, 60, 52, 58, 54, 62, 56, 60, 58, 62, 60, 62, 62, 63, 64, 96, 80, 112, 72, 98, 104, 120

Offset: 1

Author

Leroy Quet, Jul 25 2009

Keywords

• base
• nonn
• look

Comments

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.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A163381, A163382, A256999.

Programs

Maple

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

Mathematica

Table[With[{d = IntegerDigits[n, 2]}, Max@ Map[FromDigits[#, 2] &@ RotateRight[d, #] &, Range[Length@ d]]], {n, 71}] (* Michael De Vlieger, Sep 23 2017 *)

Extensions

More terms from R. J. Mathar, Aug 03 2009