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

%I A002015 #27 Feb 04 2022 11:02:11
%S A002015 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,
%T A002015 25,76,29,84,41,0,61,24,89,56,25,96,69,44,21,0,81,64,49,36,25,16,9,4,
%U A002015 1,0,1,4,9,16,25,36,49,64,81
%N A002015 a(n) = n^2 reduced mod 100.
%C A002015 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
%C A002015 A010461 gives the range of this sequence. - _Reinhard Zumkeller_, Mar 21 2010
%H A002015 <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>
%H A002015 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A002015 From _Reinhard Zumkeller_, Mar 21 2010: (Start)
%F A002015 a(n) = (n mod 10) * ((n mod 10) + 20 * ((n\10) mod 10)) mod 100.
%F A002015 a(n) = A174452(n) mod 100; A008959(n) = a(n) mod 10;
%F A002015 a(m*n) = a(m)*a(n) mod 100;
%F A002015 a(n) = (n mod 100)^2 mod 100;
%F A002015 a(n) = n for n = 0, 1, and 25. (End)
%t A002015 PowerMod[Range[0,60],2,100] (* _Harvey P. Dale_, Nov 28 2012 *)
%o A002015 (PARI) a(n)=n^2%100 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A002015 Cf. A053879, A070430, A070431, A070432, A070433, A070434, A070435, A070438, A070442, A070452, A159852.
%K A002015 nonn,easy
%O A002015 0,3
%A A002015 _N. J. A. Sloane_
%E A002015 Definition rephrased at the suggestion of _Zak Seidov_, Oct 26 2009