A174452 a(n) = n^2 mod 1000.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 24, 89, 156, 225, 296, 369, 444, 521, 600, 681, 764, 849, 936, 25, 116, 209, 304, 401, 500, 601, 704, 809, 916, 25

Offset: 0

Author

Reinhard Zumkeller, Mar 21 2010

Keywords

• nonn
• easy
• look

Comments

a(n) = A000290(n) for n < 32, but a(32) = 24;

A008959(n) = a(n) mod 10; A002015(n) = a(n) mod 100;

periodic with period 500: a(n+500)=a(n) and a(250*n+k)=a(250*n-k) for k <= 250*n;

a(n) = (n mod 1000)^2 mod 1000;

a(m*n) = a(m)*a(n) mod 1000;

A122986 gives the range of this sequence;

a(n) = n for n = 0, 1, and 376.

Examples

			Some calculations for n=982451653, to be realized by hand:
a(n) = (53^2 + 200*6*3) mod 1000 = 6409 mod 1000 = 409;
a(n) = (653^2) mod 1000 = 426409 mod 1000 = 409;
a(n) = a(n mod 500) = a(153) = 409;
a(n) = 965211250482432409 mod 1000 = 409.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to final digits of numbers

Crossrefs

Cf. A053879, A070430, A070431, A070432, A070433, A070434, A070435, A070438, A070442, A070452, A159852.

Programs

Haskell

a174452 = (`mod` 1000) . (^ 2)  -- Reinhard Zumkeller, Jul 06 2011

Maple

seq(n^2 mod 1000, n=0..55); # Nathaniel Johnston, Jun 22 2011

Mathematica

PowerMod[Range[0,60],2,1000] (* Harvey P. Dale, Feb 08 2022 *)

PARI

a(n)=n^2%1000 \\ Charles R Greathouse IV, Apr 06 2016

Formula

a(n) = ((n mod 100)^2 + 200 * (floor(n/100) mod 10) * (n mod 10)) mod 1000.