A248740 - OEIS

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

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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