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%I #10 May 13 2018 20:43:46
%S 1,1,1,2,1,3,2,1,5,3,2,4,1,9,5,3,6,2,7,4,1,17,9,5,10,3,11,6,2,13,7,4,
%T 8,1,33,17,9,18,5,19,10,3,21,11,6,12,2,25,13,7,14,4,15,8,1,65,33,17,
%U 34,9,35,18,5,37,19,10,20,3,41,21,11,22,6,23,12,2,49,25,13,26,7,27,14,4,29,15,8,16,1,129,65,33,66,17,67,34,9,69,35,18,36,5,73
%N a(n) = A003602(A048679(n)).
%C Positions of ones is given by the positive Fibonacci numbers: 1, 2, 3, 5, 8, 13, 21, ..., that is, A000045(n) from n >= 2 onward.
%C Positions of 2's is given by Lucas numbers larger than 3: 4, 7, 11, 18, ..., that is, A000032(n) from n >= 3 onward.
%C The restricted growth sequence transform of this sequence (almost certainly) is A003603.
%H Antti Karttunen, <a href="/A304100/b304100.txt">Table of n, a(n) for n = 1..17710</a>
%F a(n) = A003602(A048679(n)).
%F For all i, j: a(i) = a(j) => A304101(i) = A304101(j).
%o (PARI)
%o A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649
%o A003714(n) = { my(s=0,w); while(n>2, w = A072649(n); s += 2^(w-1); n -= fibonacci(w+1)); (s+n); }
%o A007814(n) = valuation(n,2);
%o A000265(n) = (n/2^valuation(n, 2));
%o A106151(n) = if(n<=1,n,if(n%2,1+(2*A106151((n-1)/2)),(2^(A007814(n)-1))*A106151(A000265(n))));
%o A048679(n) = if(!n,n,A106151(2*A003714(n)));
%o A003602(n) = (1+A000265(n))/2;
%o A304100(n) = A003602(A048679(n));
%Y Cf. A000032, A000045, A003602, A003603, A035513, A048679, A304101.
%K nonn
%O 1,4
%A _Antti Karttunen_, May 13 2018
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