A002708 a(n) = Fibonacci(n) mod n.

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

T. D. Noe and 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) ];
# second Maple program:
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

Adjacent sequences: A002705 A002706 A002707 * A002709 A002710 A002711

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