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A063010 Carryless binary square of n; also Moser-de Bruijn sequence written in binary. 3

%I

%S 0,1,100,101,10000,10001,10100,10101,1000000,1000001,1000100,1000101,

%T 1010000,1010001,1010100,1010101,100000000,100000001,100000100,

%U 100000101,100010000,100010001,100010100,100010101,101000000,101000001

%N Carryless binary square of n; also Moser-de Bruijn sequence written in binary.

%C Numbers that are sums of distinct powers of 100. - _David Wasserman_, Feb 26 2008

%H David Applegate, Marc LeBrun and N. J. A. Sloane, <a href="http://neilsloane.com/doc/carry1.pdf">Carryless Arithmetic (I): The Mod 10 Version</a>

%F a(n)=A062033(n)/10 i.e. with final zero removed.

%F a(n)=Sum_k>=0 {A030308(n,k)*A098608(k)}. - From _Philippe Deléham_, Oct 15 2011.

%F G.f.: (1/(1 - x))*Sum_{k>=0} 100^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017

%e a(11)=1000101, since 11 in binary is 1011 and binary carryless sum of 1011000, 0, 10110 and 1011 is 1000101.

%Y Cf. Moser-de Bruijn sequence A000695, carryless decimal squares A059729, pre-carry binary squares A063009.

%K base,nonn

%O 0,3

%A _Henry Bottomley_, Jul 03 2001

%E More terms from _David Wasserman_, Feb 26 2008

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Last modified February 18 03:43 EST 2018. Contains 299298 sequences. (Running on oeis4.)