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

0,3

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.

Links

R. Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for sequences related to final digits of numbers

Formula

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

Example

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.

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 *)

Prog

(Haskell)
a174452 = (`mod` 1000) . (^ 2)  -- Reinhard Zumkeller, Jul 06 2011
(PARI) a(n)=n^2%1000 \\ Charles R Greathouse IV, Apr 06 2016

Crossrefs

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

Sequence in context: A370785 A069821 A331221 * A174902 A000290 A162395

Adjacent sequences: A174449 A174450 A174451 * A174453 A174454 A174455

Keyword

nonn,easy,look

Author

Reinhard Zumkeller, Mar 21 2010

Status

approved