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%I #7 Nov 18 2019 16:44:08
%S 1001,11,1011,101,10011,10101,10101,111,11011,100101,100101,10111,
%T 100101,10111,10111,1001,100011,110101,110101,100111,110101,100111,
%U 100111,101001,110101,100111,100111,101001,100111,101001,101001,1011,101011,1000101,1000101,110111,1000101,110111
%N Describe n in binary: concat(c0,0,c1,1) where c0, c1 is the number of '0's and '1's in n, all written in binary.
%F a(n+1) = a(n) if n == 1 (mod 4), n > 1.
%e In the binary expansion of n = 0, we have one '0', zero '1's => a(0) = 1001.
%e In the binary expansion of n = 1, we have zero '0's, one '1' => a(0) = 0011 (leading 0's not showing up in DATA).
%e In the binary expansion of n = 2 = 10[2], we have one '0', one '1' => a(2) = 1011.
%e In the binary expansion of n = 3 = 11[2], we have zero '0's, two (= 10[2]) '1's => a(2) = 00101 (leading 0's not showing up in DATA).
%e 5 = 101[2] => a(5) = 1 0 10 1.
%e 6 = 110[2] => a(6) = 1 0 10 1: illustration of the formula.
%o (PARI) apply( {A329652(a,b=10)=fromdigits(concat([binary(logint(a+!a,2)+1-a=hammingweight(a)),0,if(a,binary(a)),1]),b)}, [0..40]) \\ 2n optional arg: base in which the string of bits is to be read - i.e., b=10: write it in binary, b=2: convert to decimal!
%Y Cf. A329653 (convert a(n) from binary to decimal), A010062.
%K nonn,base
%O 0,1
%A _M. F. Hasler_, Nov 18 2019
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