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 A216755 Digital root of the fifth power of Fibonacci(n). 0
 1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9, 7, 1, 2, 9, 5, 8, 1, 9, 1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9, 7, 1, 2, 9, 5, 8, 1, 9, 1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9, 7, 1, 2, 9, 5, 8, 1, 9, 1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9, 7, 1, 2, 9, 5, 8, 1, 9, 1, 1, 5, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This sequence is periodic with period 24, i.e. gcd(period of digital roots of squares of Fibonacci, period of digital roots of cubes of Fibonacci) LINKS Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1). FORMULA a(n) = A010888(A056572(n)). a(n) = a(n-4) - a(n-12) + a(n-16). - R. J. Mathar, Sep 15 2012 G.f. x*( -1-x-5*x^2-9*x^3-x^4-7*x^5-2*x^6-2*x^8+7*x^9-x^10-5*x^12-8*x^13-x^14-9*x^15 ) / ( (x-1) *(1+x) *(x^2+1) *(x^4+1) *(x^8-x^4+1) ). - R. J. Mathar, Sep 15 2012 MATHEMATICA (* First run program for A211821 to define digitalRoot *) Table[digitalRoot[Fibonacci[n]^5], {n, 90}] (* Alonso del Arte, Sep 15 2012 *) LinearRecurrence[{0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1}, {1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9}, 100] (* Ray Chandler, Aug 27 2015 *) CROSSREFS Cf. A030132, A216676, A216699 Sequence in context: A214395 A030125 A111698 * A255681 A021948 A306883 Adjacent sequences:  A216752 A216753 A216754 * A216756 A216757 A216758 KEYWORD nonn,base AUTHOR Ravi Bhandari, Sep 15 2012 STATUS approved

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Last modified August 20 05:25 EDT 2019. Contains 326139 sequences. (Running on oeis4.)