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A001148
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Final digit of 3^n.
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8
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1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1
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OFFSET
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0,2
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COMMENTS
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Let G = {1,3,7,9}, and let the binary operator o be defined as: X o Y = least significant digit of the product XY, where X,Y belong to G. Then (G,o) is an Abelian group and 3 is a generator of this group. - K.V.Iyer, Apr 19 2009
3^n mod 10 and 3^n mod 20. - Zerinvary Lajos, Nov 25 2009
Continued fraction expansion of (243+17*sqrt(285))/4020 = 0.13183906... (see A178148). - Klaus Brockhaus, Apr 17 2011
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LINKS
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Table of n, a(n) for n=0..80.
Index entries for sequences related to carryless arithmetic
Index entries for sequences related to final digits of numbers
Index entries for linear recurrences with constant coefficients, signature (1,-1,1).
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FORMULA
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Periodic with period 4.
From R. J. Mathar, Apr 13 2010: (Start)
a(n) = a(n-1) - a(n-2) + a(n-3).
G.f.: (1+2*x+7*x^2)/ ((1-x) * (1+x^2)). (End)
a(n) = (1/3)*(7*(n mod 4) + 4*((n+1) mod 4) - 2*((n+2) mod 4) + ((n+3) mod 4)), with n>=0. - Paolo P. Lava, May 12 2010
a(n) = 5 - (2+i)*(-i)^n - (2-i)*i^n, where i is the imaginary unit. Also a(n) = A001903(A159966(n)). - Bruno Berselli, Feb 08 2011
a(0)=1, a(1)=3, a(n) = 10 - a(n-2). - Vincenzo Librandi, Feb 08 2011
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MATHEMATICA
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Table[PowerMod[3, n, 10], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)
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PROG
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(Sage) [power_mod(3, n, 10) for n in range(0, 81)] # Zerinvary Lajos, Nov 24 2009
(MAGMA) [3^n mod 10: n in [0..150]]; // Vincenzo Librandi, Apr 12 2011
(PARI) a(n)=[1, 3, 9, 7][n%4+1] \\ Charles R Greathouse IV, Dec 27 2012
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CROSSREFS
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Sequence in context: A346108 A271879 A016676 * A262023 A275149 A011318
Adjacent sequences: A001145 A001146 A001147 * A001149 A001150 A001151
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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