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A204688
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a(n) = n^n (mod 3).
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4
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1, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1
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OFFSET
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0,6
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COMMENTS
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For n>0, a(n) is periodic with period 6: repeat [1, 1, 0, 1, 2, 0].
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LINKS
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FORMULA
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G.f.: (1+x+x^2+x^4+2*x^5-x^6) / (1-x^6). - Bruno Berselli, Jan 18 2012
a(n) = a(n-6) for n>6.
a(n) = sin(n*Pi/3) * (10*sin(n*Pi/3) + 2*sin(2*n*Pi/3) - sqrt(3) - 2*sqrt(3)*cos(n*Pi/3))/6 for n>0. (End)
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MAPLE
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MATHEMATICA
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Table[PowerMod[n, n, 3], {n, 0, 140}]
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PROG
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(Magma) [1] cat [Modexp(n, n, 3): n in [1..100]]; // Wesley Ivan Hurt, Jun 28 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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