A346080 Shadow transform of Fibonacci numbers.

0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 3, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 2, 2, 4, 1, 3, 2, 3, 2, 2, 3, 2, 1, 2, 1, 2, 3, 4, 1, 1, 2, 2, 2, 2, 6, 3, 2, 2, 2, 1, 5, 3, 3, 2, 2, 2, 1, 4, 3, 1, 2, 6, 2, 2, 1, 5, 2, 1, 2, 2, 1, 2, 1, 4, 2, 1, 4, 3, 9, 2, 2, 4

Offset

0,9

Links

Table of n, a(n) for n=0..92.

Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. See Definition 7 for the shadow transform.

OEIS Wiki, Shadow transform.

N. J. A. Sloane, Transforms.

Maple

a:= n-> add(`if`(modp(combinat[fibonacci](j), n)=0, 1, 0), j=0..n-1):
seq(a(n), n=0..100);  # Alois P. Heinz, Jul 04 2021

Mathematica

a[n_] := Sum[Boole @ Divisible[Fibonacci[i], n], {i, 0, n - 1}]; Array[a, 100, 0] (* Amiram Eldar, Jul 13 2021 *)

Prog

(Python)
from sympy import fibonacci
def a(n): return n - sum(fibonacci(k)%n != 0 for k in range(n))
print([a(n) for n in range(93)]) # Michael S. Branicky, Jul 04 2021
(PARI) a(n) = n - sum(k=0, n-1, sign(fibonacci(k)% n)); \\ Michel Marcus, Jul 04 2021

Crossrefs

Cf. A000045 (Fibonacci numbers).

Sequence in context: A309414 A007421 A239228 * A103921 A115623 A279044

Adjacent sequences: A346077 A346078 A346079 * A346081 A346082 A346083

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 04 2021

Status

approved