cp's OEIS Frontend

A257739 Numbers n for which A256999(n) > n; numbers that can be made larger by rotating (by one or more steps) the non-msb bits of their binary representation (with A080541 or A080542).

%I A257739 #20 Nov 16 2019 20:04:22
%S A257739 5,9,10,11,13,17,18,19,20,21,22,23,25,27,29,33,34,35,36,37,38,39,40,
%T A257739 41,42,43,44,45,46,47,49,50,51,53,54,55,57,59,61,65,66,67,68,69,70,71,
%U A257739 72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,97,98,99,101,102,103,105,107,108,109,110,111
%N A257739 Numbers n for which A256999(n) > n; numbers that can be made larger by rotating (by one or more steps) the non-msb bits of their binary representation (with A080541 or A080542).
%C A257739 Note that A256999(a(n)) is always in A257250.
%C A257739 If we define a co-necklace to be a finite sequence that is lexicographically maximal (not minimal) among all of its cyclic rotations, these are numbers whose binary expansion, without the most significant digit, is not a co-necklace. Numbers whose binary expansion, without the most significant digit, is not a necklace are A329367. - _Gus Wiseman_, Nov 14 2019
%H A257739 Antti Karttunen, <a href="/A257739/b257739.txt">Table of n, a(n) for n = 1..10000</a>
%e A257739 For n = 5 with binary representation "101" if we rotate other bits than the most significant bit (that is, only the two rightmost digits "01") one step to either direction we get "110" = 6 > 5, so 5 can be made larger by such rotations and thus 5 is included in this sequence.
%e A257739 For n = 6 with binary representation "110" no such rotation will yield a larger number and thus 6 is NOT included in this sequence.
%e A257739 For n = 10 with binary representation "1010" if we rotate other bits than the most significant bit (that is, only the three rightmost digits "010") either one step to the left or two steps to the right we get "1100" = 12 > 10, thus 10 is included in this sequence.
%t A257739 reckQ[q_]:=Array[OrderedQ[{RotateRight[q,#],q}]&,Length[q]-1,1,And];
%t A257739 Select[Range[2,100],!reckQ[Rest[IntegerDigits[#,2]]]&] (* _Gus Wiseman_, Nov 14 2019 *)
%o A257739 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A257739 (define A257739 (MATCHING-POS 1 1 (lambda (n) (< n (A256999 n)))))
%Y A257739 Complement: A257250.
%Y A257739 Cf. A080541, A080542, A256999.
%Y A257739 Numbers whose binary expansion is a necklace are A275692.
%Y A257739 Numbers whose binary expansion is a co-necklace are A065609.
%Y A257739 Numbers whose reversed binary expansion is a necklace are A328595.
%Y A257739 Numbers whose non-msb expansion is a co-necklace are A257250.
%Y A257739 Numbers whose non-msb expansion is a necklace are A328668.
%Y A257739 Numbers whose reversed non-msb expansion is a necklace are A328607.
%Y A257739 Numbers whose non-msb expansion is not a necklace are A329367.
%Y A257739 Binary necklaces are A000031.
%Y A257739 Necklace compositions are A008965.
%Y A257739 Cf. A000120, A001037, A003714, A014081, A121016, A164707, A328594, A328596.
%K A257739 nonn,base
%O A257739 1,1
%A A257739 _Antti Karttunen_, May 18 2015