A227896 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).

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

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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).

Formula

From Colin Barker, Sep 21 2019: (Start)

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)

Prog

(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
(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

Crossrefs

Cf. A007775, A030132.

Sequence in context: A200395 A064927 A343881 * A114610 A200390 A137209

Adjacent sequences: A227893 A227894 A227895 * A227897 A227898 A227899

Keyword

nonn,base,easy,less

Author

Gary Croft, Oct 14 2013

Status

approved