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A328847 Number of terms in Zeckendorf expansion needed to write the first Fibonacci based variant of arithmetic derivative of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)