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A001148
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Final digit of 3^n.
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9
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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
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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FORMULA
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Periodic with period 4.
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)
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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STATUS
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approved
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