A248740 a(n) = Fibonacci(n) mod 1000.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 597, 584, 181, 765, 946, 711, 657, 368, 25, 393, 418, 811, 229, 40, 269, 309, 578, 887, 465, 352, 817, 169, 986, 155, 141, 296, 437, 733, 170, 903, 73, 976, 49, 25, 74, 99, 173, 272

Offset

0,4

Comments

The sequence is periodic with period 1500 = A001175(1000).

A number m of {0, 1, ..., 999} is not in the range of this sequence, iff m is congruent to 4 or 6 mod 8.

These numbers are the 250 = 1000 - A066853(1000) numbers of the set {4, 6, 12, 14, ..., 996, 998}. E.g., a Fibonacci number will never end in the digits '100'.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, order 1500.

Formula

a(n) = (a(n-1) + a(n-2)) mod 1000 for n>1, a(0) = 0, a(1) = 1.

Example

a(17) = (a(16) + a(15)) mod 1000 = (987 + 610) mod 1000 = 1597 mod 1000 = 597.

Maple

a:= proc(n) option remember;
      `if`(n<2, n, irem(a(n-1)+a(n-2), 1000))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Oct 18 2015

Prog

(Magma) [Fibonacci(n) mod 1000: n in [0..80]]; // Vincenzo Librandi, Oct 17 2014
(PARI) vector(100, n, fibonacci(n-1)%1000) \\ Derek Orr, Oct 17 2014

Crossrefs

Cf. A000045, A003893, A105471.

Sequence in context: A000044 A107358 A243063 * A185357 A132636 A152163

Adjacent sequences: A248737 A248738 A248739 * A248741 A248742 A248743

Keyword

nonn

Author

Franz Vrabec, Oct 13 2014

Extensions

More terms from Vincenzo Librandi, Oct 17 2014

Status

approved