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Write n in base 2, complement each digit (d -> 1-d) and append the complemented digits to the sequence.
3

%I #31 Feb 16 2025 08:32:35

%S 1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0,0,1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,

%T 0,0,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,1,1,1,1,0,1,1,1,0,0,1,1,0,1,0,1,1,

%U 0,0,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,0

%N Write n in base 2, complement each digit (d -> 1-d) and append the complemented digits to the sequence.

%H Harvey P. Dale, <a href="/A030315/b030315.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric W. Weisstein, <a href="https://mathworld.wolfram.com/ChampernowneConstant.html">Champernowne Constant</a>.

%F a(n) = 1 - A030190(n). - _Amiram Eldar_, May 22 2023

%e To get the initial terms:

%e 0 -> 1

%e 1 -> 0

%e 2 = 10 -> 0, 1

%e 3 = 11 -> 0, 0

%e 4 = 100 -> 0, 0, 1

%e 5 = 101 -> 0, 1, 0,

%e ...

%e and concatenating 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, ... gives the start of the sequence. - _N. J. A. Sloane_, Jan 30 2023

%t Table[IntegerDigits[n,2]/.{1->0,0->1},{n,0,30}]//Flatten (* _Harvey P. Dale_, Jan 30 2023 *)

%Y Cf. A030190, A180433. [_Jonathan Vos Post_, Sep 05 2010]

%K nonn,base,changed

%O 0,1

%A _Clark Kimberling_

%E a(0)=1 added by _Jonathan Vos Post_, Sep 05 2010

%E Edited by _N. J. A. Sloane_, Jan 30 2023