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A044951 Numbers with no two equally numerous base 2 digits. 6


%S 1,3,4,5,6,7,8,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,

%T 30,31,32,33,34,36,39,40,43,45,46,47,48,51,53,54,55,57,58,59,60,61,62,

%U 63,64,65,66,67,68,69,70,71,72,73,74,75,76,77

%N Numbers with no two equally numerous base 2 digits.

%H Michael De Vlieger, <a href="/A044951/b044951.txt">Table of n, a(n) for n = 1..14031</a> (all terms k <= 2^14).

%H Jason Bell, Thomas Finn Lidbetter, Jeffrey Shallit, <a href="https://arxiv.org/abs/1804.07996">Additive Number Theory via Approximation by Regular Languages</a>, arXiv:1804.07996 [cs.FL], 2018.

%H Thomas Finn Lidbetter, <a href="https://uwspace.uwaterloo.ca/bitstream/handle/10012/14254/Lidbetter_Thomas.pdf">Counting, Adding, and Regular Languages</a>, Master's Thesis, University of Waterloo, Ontario, Canada, 2018.

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) ~ n. - _Charles R Greathouse IV_, Apr 18 2020

%e From _Michael De Vlieger_, Feb 07 2019: (Start)

%e 11 (binary 1011) has more 1's than 0's, thus it is in the sequence.

%e 12 (binary 1100) has an equal number of 0's and 1's, thus it is not in the sequence.

%e (End)

%t Select[Range@ 77, UnsameQ @@ DigitCount[#, 2] &] (* _Michael De Vlieger_, Feb 07 2019 *)

%o (PARI) is(n)=2*hammingweight(n)!=exponent(n)+1 \\ _Charles R Greathouse IV_, Apr 18 2020

%Y Cf. A072600 (#0's < #1's), A072601 (#0's <= #1's), A031443 (#0's = #1's).

%Y Cf. A072602 (#0's >= #1's), A072603 (#0's > #1's), this sequence (#0's <> #1's).

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)