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

Author

Franz Vrabec, Oct 13 2014

Keywords

• nonn

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'.

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3000
• Index entries for linear recurrences with constant coefficients, order 1500.

Crossrefs

Cf. A000045, A003893, A105471.

Programs

Magma

[Fibonacci(n) mod 1000: n in [0..80]]; // Vincenzo Librandi, Oct 17 2014

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

PARI

vector(100,n,fibonacci(n-1)%1000) \\ Derek Orr, Oct 17 2014

Formula

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

Extensions

More terms from Vincenzo Librandi, Oct 17 2014