A328847 Number of terms in Zeckendorf expansion needed to write the first Fibonacci based variant of arithmetic derivative of n.

0, 0, 1, 1, 2, 1, 2, 1, 3, 3, 2, 1, 3, 1, 4, 3, 3, 1, 4, 1, 3, 4, 4, 1, 3, 3, 3, 4, 4, 1, 3, 1, 4, 3, 5, 3, 3, 1, 5, 4, 3, 1, 4, 1, 3, 3, 4, 1, 3, 4, 3, 3, 6, 1, 5, 3, 4, 5, 4, 1, 3, 1, 5, 3, 4, 4, 2, 1, 5, 6, 2, 1, 3, 1, 4, 3, 5, 5, 5, 1, 3, 5, 5, 1, 3, 7, 5, 4, 3, 1, 3, 5, 5, 5, 4, 6, 4, 1, 3, 4, 5, 1, 7, 1, 6, 5

Offset

0,5

Links

Antti Karttunen, Table of n, a(n) for n = 0..20000

Formula

a(n) = A007895(A328845(n)).

a(p) = 1 for all primes p.

Prog

(PARI)
A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i, 1])/f[i, 1]));
A007895(n) = { my(s=0); while(n>0, s++; n -= fibonacci(1+A072649(n))); (s); }
A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649
A328847(n) = A007895(A328845(n));

Crossrefs

Cf. A000045, A007895, A324907, A328845.

Sequence in context: A270096 A039636 A322866 * A331175 A331954 A309892

Adjacent sequences: A328844 A328845 A328846 * A328848 A328849 A328850

Keyword

nonn

Author

Antti Karttunen, Oct 28 2019

Status

approved