A324905 -id:A324905 - cp's OEIS frontend

A324907 a(n) = A007895(A113175(n)).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 3, 2, 1, 1, 1, 3, 1, 2, 1, 1, 2, 1, 1, 3, 1, 3, 2, 1, 1, 2, 3, 1, 2, 1, 1, 3, 1, 4, 2, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 3, 4, 1, 2, 1, 3, 1, 1, 4, 3, 3, 1, 2, 1, 1, 4

Offset: 1

Antti Karttunen, Apr 14 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..17711

Cf. A113175, A007895, A300837, A324888, A324905.

A113175(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = fibonacci(f[i, 1])); factorback(f); };
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
A324907(n) = A007895(A113175(n));

a(n) = A007895(A113175(n)).

a(2n) = a(n).

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

Original entry on oeis.org

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

Antti Karttunen, Oct 29 2019

nonn

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

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

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));

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

A324901 a(n) = A007895(A324900(n)).

Original entry on oeis.org

1, 2, 2, 3, 2, 3, 2, 3, 3, 4, 2, 4, 2, 4, 3, 6, 2, 5, 2, 5, 4, 4, 2, 6, 3, 4, 6, 5, 2, 3, 2, 7, 4, 4, 3, 7, 2, 4, 4, 5, 2, 7, 2, 6, 6, 4, 2, 7, 3, 6, 4, 6, 2, 5, 4, 4, 4, 4, 2, 5, 2, 4, 5, 7, 4, 7, 2, 6, 4, 5, 2, 8, 2, 4, 5, 6, 3, 8, 2, 9, 8, 4, 2, 5, 4, 4, 4, 11, 2, 6, 4, 6, 4, 4, 4, 10, 2, 6, 5, 5, 2, 8, 2, 11, 8

Offset: 1

Antti Karttunen, Apr 15 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences computed from indices in prime factorization

Cf. A000032, A007895, A324900, A324905, A324907.

A000032(n) = (fibonacci(n+1)+fibonacci(n-1));
A324900(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = A000032(2*(1+primepi(f[i, 1])))); factorback(f); };
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
A324901(n) = A007895(A324900(n));

a(n) = A007895(A324900(n)).

cp's OEIS Frontend

A324907 a(n) = A007895(A113175(n)).

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

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A324901 a(n) = A007895(A324900(n)).

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