A304100 a(n) = A003602(A048679(n)).

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, 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, 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

Offset: 1

Author

Antti Karttunen, May 13 2018

Keywords

• nonn

Comments

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.

Positions of 2's is given by Lucas numbers larger than 3: 4, 7, 11, 18, ..., that is, A000032(n) from n >= 3 onward.

The restricted growth sequence transform of this sequence (almost certainly) is A003603.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..17710

Crossrefs

Cf. A000032, A000045, A003602, A003603, A035513, A048679, A304101.

Programs

PARI

A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649
A003714(n) = { my(s=0,w); while(n>2, w = A072649(n); s += 2^(w-1); n -= fibonacci(w+1)); (s+n); }
A007814(n) = valuation(n,2);
A000265(n) = (n/2^valuation(n, 2));
A106151(n) = if(n<=1,n,if(n%2,1+(2*A106151((n-1)/2)),(2^(A007814(n)-1))*A106151(A000265(n))));
A048679(n) = if(!n,n,A106151(2*A003714(n)));
A003602(n) = (1+A000265(n))/2;
A304100(n) = A003602(A048679(n));

Formula

a(n) = A003602(A048679(n)).

For all i, j: a(i) = a(j) => A304101(i) = A304101(j).