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

Offset: 1

Author

Sergio Pimentel, Sep 22 2006

Keywords

• base
• fini
• full
• easy
• nonn

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.

Examples

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

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

Crossrefs

Cf. A036688, A010382, A010411, A010462, A010421, A174452.

Cf. A006716, A053975, A027676, A027678, A122987, A122988.

Row 1000 of A096008.

Programs

Magma

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

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 *)

Extensions

More terms and additional comments from Reinhard Zumkeller, Mar 21 2010

Edited by N. J. A. Sloane, Apr 10 2010