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%I #22 Aug 27 2015 11:35:06
%S 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,
%T 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,
%U 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
%N Digital root of the fifth power of Fibonacci(n).
%C 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)
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1).
%F a(n) = A010888(A056572(n)).
%F a(n) = a(n-4) - a(n-12) + a(n-16). - _R. J. Mathar_, Sep 15 2012
%F 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
%t (* First run program for A211821 to define digitalRoot *) Table[digitalRoot[Fibonacci[n]^5], {n, 90}] (* _Alonso del Arte_, Sep 15 2012 *)
%t 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 *)
%Y Cf. A030132, A216676, A216699
%K nonn,base
%O 1,3
%A _Ravi Bhandari_, Sep 15 2012
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