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

0,3

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

Table of n, a(n) for n=0..59.

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).

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)

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A066308 A063462 A098736 * A257587 A257588 A352598

Adjacent sequences: A002012 A002013 A002014 * A002016 A002017 A002018

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved