A002015 a(n) = n^2 reduced mod 100.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 21, 44, 69, 96, 25, 56, 89, 24, 61, 0, 41, 84, 29, 76, 25, 76, 29, 84, 41, 0, 61, 24, 89, 56, 25, 96, 69, 44, 21, 0, 81, 64, 49, 36, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Periodic with period 50: (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 21, 44, 69, 96, 25, 56, 89, 24, 61, 0, 41, 84, 29, 76, 25, 76, 29, 84, 41, 0, 61, 24, 89, 56, 25, 96, 69, 44, 21, 0, 81, 64, 49, 36, 25, 16, 9, 4, 1) and next term is 0. The period is symmetrical about the "midpoint" 25. - Zak Seidov, Oct 26 2009

A010461 gives the range of this sequence. - Reinhard Zumkeller, Mar 21 2010

Links

• Index entries for sequences related to final digits of numbers
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

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

Programs

Mathematica

PowerMod[Range[0,60],2,100] (* Harvey P. Dale, Nov 28 2012 *)

PARI

a(n)=n^2%100 \\ Charles R Greathouse IV, Oct 07 2015

Formula

From Reinhard Zumkeller, Mar 21 2010: (Start)

a(n) = (n mod 10) * ((n mod 10) + 20 * ((n\10) mod 10)) mod 100.

a(n) = A174452(n) mod 100; A008959(n) = a(n) mod 10;

a(m*n) = a(m)*a(n) mod 100;

a(n) = (n mod 100)^2 mod 100;

a(n) = n for n = 0, 1, and 25. (End)

Extensions

Definition rephrased at the suggestion of Zak Seidov, Oct 26 2009