A328848 Number of terms in Zeckendorf expansion needed to write the second Fibonacci based variant of arithmetic derivative of n.

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

Offset

0,7

Links

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

Formula

a(n) = A007895(A328846(n)).

Prog

(PARI)
A328846(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(2+primepi(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
A328848(n) = A007895(A328846(n));

Crossrefs

Cf. A000045, A007895, A324905, A328846, A328847.

Sequence in context: A343950 A085247 A003016 * A108121 A161916 A072548

Adjacent sequences: A328845 A328846 A328847 * A328849 A328850 A328851

Keyword

nonn

Author

Antti Karttunen, Oct 29 2019

Status

approved