%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 Moserde 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 DelĂ©ham_, 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. Moserde Bruijn sequence A000695, carryless decimal squares A059729, precarry binary squares A063009.
%K base,nonn
%O 0,3
%A _Henry Bottomley_, Jul 03 2001
%E More terms from _David Wasserman_, Feb 26 2008
