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

1,2

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A163381, A163382, A256999.

Sequence in context: A246594 A175808 A334666 * A233569 A246593 A256999

Adjacent sequences: A163377 A163378 A163379 * A163381 A163382 A163383

Keyword

base,nonn,look

Author

Leroy Quet, Jul 25 2009

Extensions

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

Status

approved