A122986 - OEIS

A122986

Squares mod 1000.

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

(list; graph; refs; listen; history; text; internal format)

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