

A275692


Every rotation of the binary digits of n is less than n.


1



0, 1, 2, 4, 6, 8, 12, 14, 16, 20, 24, 26, 28, 30, 32, 40, 48, 50, 52, 56, 58, 60, 62, 64, 72, 80, 84, 96, 98, 100, 104, 106, 108, 112, 114, 116, 118, 120, 122, 124, 126, 128, 144, 160, 164, 168, 192, 194, 196, 200, 202, 208, 210, 212, 216, 218, 224, 226, 228
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OFFSET

1,3


COMMENTS

0, and members of A065609 that are not in A121016.
Number of terms with d binary digits is A001037(d).
Take the binary representation of a(n), reverse it, add 1 to each digit. The result is the decimal representation of A102659(n).


LINKS

Robert Israel, Table of n, a(n) for n = 1..9868


EXAMPLE

6 is in the sequence because its binary representation 110 is greater than all the rotations 011 and 101.
10 is not in the sequence because its binary representation 1010 is unchanged under rotation by 2 places.


MAPLE

filter:= proc(n) local L, k;
L:= convert(convert(n, binary), string);
for k from 1 to length(L)1 do
if lexorder(L, StringTools:Rotate(L, k)) then return false fi;
od;
true
end proc:
select(filter, [$0..1000]);


MATHEMATICA

filterQ[n_] := Module[{bits, rr}, bits = IntegerDigits[n, 2]; rr = NestList[RotateRight, bits, Length[bits]1] // Rest; AllTrue[rr, FromDigits[#, 2] < n&]];
Select[Range[0, 1000], filterQ] (* JeanFrançois Alcover, Apr 29 2019 *)


CROSSREFS

Cf. A001037, A065609, A102659, A121016.
Sequence in context: A318186 A139363 A091065 * A163823 A015929 A043723
Adjacent sequences: A275689 A275690 A275691 * A275693 A275694 A275695


KEYWORD

nonn


AUTHOR

Robert Israel, Aug 05 2016


STATUS

approved



