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A227896
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32-beat repeating palindromic sequence: digital roots of Fibonacci numbers indexed by the set of natural numbers not divisible by 2, 3 or 5 (A007775).
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3
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1, 4, 8, 8, 4, 5, 1, 5, 4, 8, 4, 5, 1, 1, 5, 8, 8, 5, 1, 1, 5, 4, 8, 4, 5, 1, 5, 4, 8, 8, 4, 1, 1, 4, 8, 8, 4, 5, 1, 5, 4, 8, 4, 5, 1, 1, 5, 8, 8, 5, 1, 1, 5, 4, 8, 4, 5, 1, 5, 4, 8, 8, 4, 1, 1, 4, 8, 8, 4, 5, 1, 5, 4, 8, 4, 5, 1, 1, 5, 8, 8, 5, 1, 1, 5, 4, 8, 4, 5, 1, 5, 4, 8, 8, 4, 1, 1, 4, 8, 8, 4, 5, 1, 5, 4, 8, 4, 5, 1, 1, 5, 8, 8, 5, 1, 1, 5, 4, 8, 4, 5, 1, 5, 4, 8, 8, 4, 1
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OFFSET
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1,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
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FORMULA
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G.f.: x*(1 + 3*x + 4*x^2 - 4*x^4 + x^5 - 4*x^6 + 4*x^7 - x^8 + 4*x^9 - 4*x^10 + x^11 - 4*x^12 + 4*x^14 + 3*x^15 + x^16) / ((1 - x)*(1 + x^16)).
a(n) = a(n-1) - a(n-16) + a(n-17) for n>17.
(End)
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PROG
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(PARI) a(n)=[1, 4, 8, 8, 4, 5, 1, 5, 4, 8, 4, 5, 1, 1, 5, 8, 8, 5, 1, 1, 5, 4, 8, 4, 5, 1, 5, 4, 8, 8, 4, 1][n%32+1] \\ Charles R Greathouse IV, Aug 26 2014
(PARI) Vec(x*(1 + 3*x + 4*x^2 - 4*x^4 + x^5 - 4*x^6 + 4*x^7 - x^8 + 4*x^9 - 4*x^10 + x^11 - 4*x^12 + 4*x^14 + 3*x^15 + x^16) / ((1 - x)*(1 + x^16)) + O(x^100)) \\ Colin Barker, Sep 21 2019
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CROSSREFS
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KEYWORD
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nonn,base,easy,less
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AUTHOR
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STATUS
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approved
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