

A122986


Squares mod 1000.


9



0, 1, 4, 9, 16, 24, 25, 36, 41, 44, 49, 56, 64, 76, 81, 84, 89, 96, 100, 104, 116, 121, 124, 129, 136, 144, 156, 161, 164, 169, 176, 184, 196, 201, 204, 209, 216, 224, 225, 236, 241, 244, 249, 256, 264, 276, 281, 284, 289, 296, 304, 316, 321, 324, 329, 336, 344
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OFFSET

1,3


COMMENTS

Possible last three digits of n^2 (leading zeros omitted).
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.


LINKS

R. Zumkeller, Table of n, a(n) for n = 1..159 (full sequence)
Eric Weisstein's World of Mathematics, Square Numbers.
Index entries for sequences related to final digits of numbers


EXAMPLE

The last three digits of n^2 can be 000, 001, 236, 241, 996, etc. but not 002, 003, 237, 238, etc.


MAPLE

s:={}: for n from 0 to 999 do s:=s union {n^2 mod 1000}: od: op(s); # Nathaniel Johnston, Jun 22 2011


MATHEMATICA

Union[PowerMod[Range[1000], 2, 1000]] (* Vincenzo Librandi, Dec 29 2019 *)


PROG

(MAGMA) [n: n in [0..999]  IsSquare(R! n) where R:= ResidueClassRing(1000)]; // Vincenzo Librandi, Dec 29 2019


CROSSREFS

Cf. A036688, A010382, A010411, A010462, A010421, A174452.
Cf. A006716, A053975, A027676, A027678, A122987, A122988.
Row 1000 of A096008.
Sequence in context: A176238 A139588 A320894 * A066427 A320891 A161697
Adjacent sequences: A122983 A122984 A122985 * A122987 A122988 A122989


KEYWORD

base,fini,full,easy,nonn


AUTHOR

Sergio Pimentel, Sep 22 2006


EXTENSIONS

More terms and additional comments from Reinhard Zumkeller, Mar 21 2010
Edited by N. J. A. Sloane, Apr 10 2010


STATUS

approved



