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

%I A248740 #20 Sep 08 2022 08:46:10
%S A248740 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,597,584,181,765,946,
%T A248740 711,657,368,25,393,418,811,229,40,269,309,578,887,465,352,817,169,
%U A248740 986,155,141,296,437,733,170,903,73,976,49,25,74,99,173,272
%N A248740 a(n) = Fibonacci(n) mod 1000.
%C A248740 The sequence is periodic with period 1500 = A001175(1000).
%C A248740 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.
%C A248740 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'.
%H A248740 Alois P. Heinz, <a href="/A248740/b248740.txt">Table of n, a(n) for n = 0..3000</a>
%H A248740 <a href="/index/Rec#order_1500">Index entries for linear recurrences with constant coefficients</a>, order 1500.
%F A248740 a(n) = (a(n-1) + a(n-2)) mod 1000 for n>1, a(0) = 0, a(1) = 1.
%e A248740 a(17) = (a(16) + a(15)) mod 1000 = (987 + 610) mod 1000 = 1597 mod 1000 = 597.
%p A248740 a:= proc(n) option remember;
%p A248740       `if`(n<2, n, irem(a(n-1)+a(n-2), 1000))
%p A248740     end:
%p A248740 seq(a(n), n=0..60);  # _Alois P. Heinz_, Oct 18 2015
%o A248740 (Magma) [Fibonacci(n) mod 1000: n in [0..80]]; // _Vincenzo Librandi_, Oct 17 2014
%o A248740 (PARI) vector(100,n,fibonacci(n-1)%1000) \\ _Derek Orr_, Oct 17 2014
%Y A248740 Cf. A000045, A003893, A105471.
%K A248740 nonn
%O A248740 0,4
%A A248740 _Franz Vrabec_, Oct 13 2014
%E A248740 More terms from _Vincenzo Librandi_, Oct 17 2014