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%I #30 Aug 02 2021 09:22:07
%S 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,
%T 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,
%U 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
%N 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).
%H Colin Barker, <a href="/A227896/b227896.txt">Table of n, a(n) for n = 1..1000</a>
%H Gary W. Croft, <a href="https://www.primesdemystified.com/twinprimes.html">Twin Primes Demystified</a>
%H Gary W. Croft, <a href="https://www.primesdemystified.com/Fibo_Digital_Root_Multiplication_Matrix.jpg">Digital Root Multiplication Matrix Produced by this Sequence</a>
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
%F From _Colin Barker_, Sep 21 2019: (Start)
%F 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)).
%F a(n) = a(n-1) - a(n-16) + a(n-17) for n>17.
%F (End)
%o (PARI) a(n)=fibonacci(n\8*6 + 9 + 3*(n+1)\2*2 - max(5, (n-2)%8)*2)%9 \\ _Charles R Greathouse IV_, Aug 26 2014
%o (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
%o (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
%Y Cf. A007775, A030132.
%K nonn,base,easy,less
%O 1,2
%A _Gary Croft_, Oct 14 2013
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