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A328848 Number of terms in Zeckendorf expansion needed to write the second Fibonacci based variant of arithmetic derivative of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A144148 A085247 A003016 * A108121 A161916 A072548

Adjacent sequences:  A328845 A328846 A328847 * A328849 A328850 A328851

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 29 2019

STATUS

approved

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Last modified August 14 01:55 EDT 2020. Contains 336476 sequences. (Running on oeis4.)