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A079344
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F(n) mod 8, where F(n) = A000045(n) is the n-th Fibonacci number.
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10
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0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5
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OFFSET
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0,4
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COMMENTS
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This sequence does not contain the complete set of residues modulo 8. See A079002. - Michel Marcus, Jan 31 2020
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LINKS
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FORMULA
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Sequence is periodic with Pisano period 12 = A001175(8).
G.f.: -x*(1+x^2+x^3+3*x^4+6*x^6-5*x^5+x^7) / ( (x-1)*(x^2-x+1)*(1+x+x^2)*(x^4-x^2+1) ). - R. J. Mathar, Aug 08 2012
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EXAMPLE
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a(8) = F(8) mod 8 = 21 mod 8 = 5.
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MATHEMATICA
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Mod[Fibonacci[Range[0, 110]], 8] (* or *) LinearRecurrence[ {1, 0, 0, -1, 1, 0, 0, -1, 1}, {0, 1, 1, 2, 3, 5, 0, 5, 5}, 110] (* Harvey P. Dale, Jan 16 2014 *)
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PROG
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(PARI) for (n=0, 100, print1(fibonacci(n)%8", "))
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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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EXTENSIONS
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STATUS
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approved
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