

A163381


a(n) = the (decimal equivalent of the) smallest integer that can be made by rotating the binary digits of n any number of positions to the left or right. a(n) in binary may contain fewer digits, after leading 0's are removed, than n written in binary has.


5



1, 1, 3, 1, 3, 3, 7, 1, 3, 5, 7, 3, 7, 7, 15, 1, 3, 5, 7, 5, 11, 11, 15, 3, 7, 11, 15, 7, 15, 15, 31, 1, 3, 5, 7, 9, 11, 13, 15, 5, 13, 21, 23, 11, 27, 23, 31, 3, 7, 11, 15, 13, 23, 27, 31, 7, 15, 23, 31, 15, 31, 31, 63, 1, 3, 5, 7, 9, 11, 13, 15, 9, 19, 21, 23, 19, 27, 29, 31, 5, 13, 21, 29
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OFFSET

1,3


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..8190


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. 7 is the smallest of these, so a(13) = 7.


MAPLE

a:= proc(n) local i, k, m, s;
k, m, s:= ilog2(n), n, n;
for i to k do m:= iquo(m, 2, 'd') +d*2^k; s:=s, m od;
min(s)
end:
seq(a(n), n=1..80); # Alois P. Heinz, May 24 2012


MATHEMATICA

Table[Min[FromDigits[ #, 2]&/@ NestList[RotateLeft, IntegerDigits[n, 2], Floor[Log[2, n]]]], {n, 255}] (* Wouter Meeussen, Jul 27 2009 *)


PROG

(PARI) a(n)=local(k=#binary(n), m=2^k, t=n*(m+1)); vecmin(vector(k, x, (t\2^x)%m)) \\ Hagen von Eitzen, Jul 27 2009


CROSSREFS

Cf. A163380, A163382.
Sequence in context: A173465 A151837 A331856 * A327190 A160123 A238784
Adjacent sequences: A163378 A163379 A163380 * A163382 A163383 A163384


KEYWORD

base,nonn,look


AUTHOR

Leroy Quet, Jul 25 2009


EXTENSIONS

More terms from Hagen von Eitzen and Wouter Meeussen, Jul 27 2009


STATUS

approved



