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%I #81 Sep 08 2022 08:44:50
%S 0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,1,1,
%T 1,1,0,0,1,1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,1,1,0,0,1,0,1,0,0,
%U 1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,1,0
%N Binary Champernowne sequence (or word): write the numbers 0,1,2,3,4,... in base 2 and juxtapose.
%C a(A003607(n)) = 0 and for n > 0: a(A030303(n)) = 1. - _Reinhard Zumkeller_, Dec 11 2011
%C An irregular table in which the n-th row lists the bits of n (see the example section). - _Jason Kimberley_, Dec 07 2012
%C The binary Champernowne constant: it is normal in base 2. - _Jason Kimberley_, Dec 07 2012
%C This is the characteristic function of A030303, which gives the indices of 1's in this sequence and has first differences given by A066099. - _M. F. Hasler_, Oct 12 2020
%D Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.
%H Reinhard Zumkeller, <a href="/A030190/b030190.txt">Table of n, a(n) for n = 0..10000</a>
%H Jean Berstel, <a href="http://www-igm.univ-mlv.fr/~berstel/">Home Page</a> (in case the following link should be broken)
%H Jean Berstel and Juhani Karhumäki, <a href="http://www-igm.univ-mlv.fr/~berstel/Articles/2003TutorialCoWdec03.pdf">Combinatorics on words-a tutorial</a>. Bull. Eur. Assoc. Theor. Comput. Sci. EATCS, # 79, pp. 178-228, 2003.
%H S. Ferenczi, <a href="http://dx.doi.org/10.1016/S0012-365X(98)00400-2">Complexity of sequences and dynamical systems</a>, Discrete Math., 206 (1999), 145-154.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BinaryChampernowneConstant.html">Binary Champernowne Constant</a>
%e As an array, this begins:
%e 0,
%e 1,
%e 1, 0,
%e 1, 1,
%e 1, 0, 0,
%e 1, 0, 1,
%e 1, 1, 0,
%e 1, 1, 1,
%e 1, 0, 0, 0,
%e 1, 0, 0, 1,
%e 1, 0, 1, 0,
%e 1, 0, 1, 1,
%e 1, 1, 0, 0,
%e 1, 1, 0, 1,
%e 1, 1, 1, 0,
%e 1, 1, 1, 1,
%e 1, 0, 0, 0, 0,
%e 1, 0, 0, 0, 1,
%e ...
%t Flatten[ Table[ IntegerDigits[n, 2], {n, 0, 26}]] (* _Robert G. Wilson v_, Mar 08 2005 *)
%o (Haskell)
%o import Data.List (unfoldr)
%o a030190 n = a030190_list !! n
%o a030190_list = concatMap reverse a030308_tabf
%o -- _Reinhard Zumkeller_, Jun 16 2012, Dec 11 2011
%o (Magma) [0]cat &cat[Reverse(IntegerToSequence(n,2)):n in[1..31]]; // _Jason Kimberley_, Dec 07 2012
%o (PARI) A030190_row(n)=if(n,binary(n),[0]) \\ _M. F. Hasler_, Oct 12 2020
%o (Python)
%o from itertools import count, islice
%o def A030190_gen(): return (int(d) for m in count(0) for d in bin(m)[2:])
%o A030190_list = list(islice(A030190_gen(),30)) # _Chai Wah Wu_, Jan 07 2022
%Y Cf. A007376, A003137, A030308. Same as and more fundamental than A030302, but I have left A030302 in the OEIS because there are several sequences that are based on it (A030303 etc.). - _N. J. A. Sloane_.
%Y a(n) = T(A030530(n), A083652(A030530(n))-n-1), T as defined in A083651, a(A083652(k))=1.
%Y Tables in which the n-th row lists the base b digits of n: this sequence and A030302 (b=2), A003137 and A054635 (b=3), A030373 (b=4), A031219 (b=5), A030548 (b=6), A030998 (b=7), A031035 and A054634 (b=8), A031076 (b=9), A007376 and A033307 (b=10). - _Jason Kimberley_, Dec 06 2012
%Y A076478 is a similar sequence.
%Y For run lengths see A056062; see also A318924.
%Y See also A066099 for (run lengths of 0s) + 1 = first difference of positions of 1s given by A030303.
%K nonn,base,cons,easy,tabf
%O 0,1
%A _Clark Kimberling_
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