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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)