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%I #22 Sep 08 2022 08:45:28
%S 0,1,4,9,16,24,25,36,41,44,49,56,64,76,81,84,89,96,100,104,116,121,
%T 124,129,136,144,156,161,164,169,176,184,196,201,204,209,216,224,225,
%U 236,241,244,249,256,264,276,281,284,289,296,304,316,321,324,329,336,344
%N Squares mod 1000.
%C Possible last three digits of n^2 (leading zeros omitted).
%C Range of A174452; A010461 is a subset; and also all squares less than 1000 belong to this sequence; the sequence is finite with A000993(3)=159 terms: a(159)=996 is the last term.
%H R. Zumkeller, <a href="/A122986/b122986.txt">Table of n, a(n) for n = 1..159</a> (full sequence)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Numbers</a>.
%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>
%e The last three digits of n^2 can be 000, 001, 236, 241, 996, etc. but not 002, 003, 237, 238, etc.
%p s:={}: for n from 0 to 999 do s:=s union {n^2 mod 1000}: od: op(s); # _Nathaniel Johnston_, Jun 22 2011
%t Union[PowerMod[Range[1000], 2, 1000]] (* _Vincenzo Librandi_, Dec 29 2019 *)
%o (Magma) [n: n in [0..999] | IsSquare(R! n) where R:= ResidueClassRing(1000)]; // _Vincenzo Librandi_, Dec 29 2019
%Y Cf. A036688, A010382, A010411, A010462, A010421, A174452.
%Y Cf. A006716, A053975, A027676, A027678, A122987, A122988.
%Y Row 1000 of A096008.
%K base,fini,full,easy,nonn
%O 1,3
%A _Sergio Pimentel_, Sep 22 2006
%E More terms and additional comments from _Reinhard Zumkeller_, Mar 21 2010
%E Edited by _N. J. A. Sloane_, Apr 10 2010
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