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A346080
Shadow transform of Fibonacci numbers.
0
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 04 2021
STATUS
approved