

A002015


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


4



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
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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
Contribution from Reinhard Zumkeller, Mar 21 2010: (Start)
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;
A010461 gives the range of this sequence;
a(n) = n for n = 0, 1, and 25. (End)


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

a(n) = (n mod 10) * ((n mod 10) + 20 * ((n\10) mod 10)) mod 100.  Reinhard Zumkeller, Mar 21 2010


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 A303269
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



