Could you verify that I have interpreted your second sequence correctly? (I dare not say: usefully) That is, summing the digits in a binary count
base 10 = binary => binary sum = digit in sequence1 = 1 => 1 = 1
2 = 10 => 1+0 = 1
3 = 11 => 1+1 = 2
4 = 100 => 1+0+0 = 1
5 = 101 => 1+0+1 = 2
6 = 110 => 1+1+0 = 2
7 = 111 => 1+1+1 = 3
8 = 1000 => 1+0+0+0 = 1
9 = 1001 => 1+0+0+1 = 2
10 = 1010 => 1+0+1+0 = 2
gives the sequence 1,1,2,1,2,2,3,1,2,2... For which you say “If you know the answer, you’d almost certainly know how to generate the sequence that begins with the following 512 numbers:”. If this is indeed the way the second sequence was meant to be interpreted then you could perhaps give a nod.
~modest
