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URL: https://oeis.org/A002708

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A002708
a(n) = Fibonacci(n) mod n.
21
0, 1, 2, 3, 0, 2, 6, 5, 7, 5, 1, 0, 12, 13, 10, 11, 16, 10, 1, 5, 5, 1, 22, 0, 0, 25, 20, 11, 1, 20, 1, 5, 13, 33, 30, 0, 36, 1, 37, 35, 1, 34, 42, 25, 20, 45, 46, 0, 36, 25, 32, 23, 52, 8, 5, 21, 40, 1, 1, 0, 1, 1, 43, 59, 60, 52, 66, 65, 44, 15, 1, 0, 72, 73, 50, 3, 2, 44, 1, 5, 7, 1, 82, 24
OFFSET
1,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002, p. 891.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 5000 terms from T. D. Noe)
E. Lucas, Théorie des nombres (annotated scans of a few selected pages)
MAPLE
with(combinat): [ seq( fibonacci(n) mod n, n=1..80) ];
# Alternative:
a:= proc(n) local r, M, p; r, M, p:=
<<1|0>, <0|1>>, <<0|1>, <1|1>>, n;
do if irem(p, 2, 'p')=1 then r:= r.M mod n fi;
if p=0 then break fi; M:= M.M mod n
od; r[1, 2]
end:
seq(a(n), n=1..100); # Alois P. Heinz, Nov 26 2016
MATHEMATICA
Table[Mod[Fibonacci[n], n], {n, 1, 100}] (* Stefan Steinerberger, Apr 18 2006 *)
PROG
(Magma) [Fibonacci(n) mod n : n in [1..120]]; // Vincenzo Librandi, Nov 19 2015
(Python)
A002708_list, a, b, = [], 1, 1
for n in range(1, 10**4+1):
A002708_list.append(a%n)
a, b = b, a+b # Chai Wah Wu, Nov 26 2015
(PARI) a(n) = fibonacci(n) % n; \\ Michel Marcus, May 11 2016
CROSSREFS
Cf. A002726, A002752, A023172 (indices of 0's), A023173 (indices of 1's), A023174-A023182.
Cf. A263101.
Main diagonal of A161553.
Sequence in context: A194745 A248342 A002392 * A167925 A209927 A354077
KEYWORD
nonn,easy,look
AUTHOR
John C. Hallyburton, Jr. (hallyb(AT)evms.ENET.dec.com)
EXTENSIONS
More terms from Stefan Steinerberger, Apr 18 2006
STATUS
approved