The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A357724 Triangular array read by rows: T(n,k) = Fib(n) mod Fib(k) for 1 <= k <= n, where Fib(k) = A000045(k). 2
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 3, 0, 0, 0, 1, 1, 3, 5, 0, 0, 0, 1, 0, 1, 5, 8, 0, 0, 0, 0, 1, 4, 2, 8, 13, 0, 0, 0, 1, 1, 0, 7, 3, 13, 21, 0, 0, 0, 1, 2, 4, 1, 11, 5, 21, 34, 0, 0, 0, 0, 0, 4, 0, 1, 18, 8, 34, 55, 0, 0, 0, 1, 2, 3, 1, 12, 2, 29, 13, 55, 89, 0, 0, 0, 1, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,14
COMMENTS
For k > 2, T(n,k) = 0 if and only if n is divisible by k. Otherwise, let n = q*k+r with 0 < r < k and k > 2.
If q is even and k is even, or q == 0 (mod 4) and k is odd, T(n,k) = A000045(r).
If q == 2 (mod 4) and k is odd, T(n,k) = A000045(k) - A000045(r).
If q == 1 (mod 4) and r is odd, or q == 3 (mod 4) and r+k is odd, T(n,k) = A000045(k-r).
If q == 1 (mod 4) and r is even, or q == 3 (mod 4) and r+k is even, T(n,k) = A000045(k) - A000045(k-r).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)
EXAMPLE
Triangle starts:
0;
0, 0;
0, 0, 0;
0, 0, 1, 0;
0, 0, 1, 2, 0;
0, 0, 0, 2, 3, 0;
0, 0, 1, 1, 3, 5, 0;
0, 0, 1, 0, 1, 5, 8, 0;
0, 0, 0, 1, 4, 2, 8, 13, 0;
0, 0, 1, 1, 0, 7, 3, 13, 21, 0;
0, 0, 1, 2, 4, 1, 11, 5, 21, 34, 0;
MAPLE
fib:= combinat:-fibonacci:
for n from 1 to 20 do
seq(fib(n) mod fib(k), k=1..n)
od;
CROSSREFS
Sequence in context: A342563 A343633 A174469 * A297934 A112166 A112167
KEYWORD
nonn,look,tabl
AUTHOR
J. M. Bergot and Robert Israel, Oct 12 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 04:02 EDT 2024. Contains 372900 sequences. (Running on oeis4.)