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Digital root of cubes of Fibonacci numbers.
2

%I #20 Aug 25 2015 13:57:33

%S 0,1,1,8,9,8,8,1,9,1,1,8,9,8,8,1,9,1,1,8,9,8,8,1,9,1,1,8,9,8,8,1,9,1,

%T 1,8,9,8,8,1,9,1,1,8,9,8,8,1,9,1,1,8,9,8,8,1,9,1,1,8,9,8,8,1,9,1,1,8,

%U 9,8,8,1,9,1,1,8,9,8,8,1,9,1,1,8,9,8,8

%N Digital root of cubes of Fibonacci numbers.

%C This sequence repeats after every 8 terms, hence this is periodic with period 8.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 1).

%t Table[NestWhile[Total[IntegerDigits[#]] &, Fibonacci[n]^3, # > 9 &], {n, 0, 86}] (* _T. D. Noe_, Oct 15 2012 *)

%t Join[{0},LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1},{1, 1, 8, 9, 8, 8, 1, 9},86]] (* _Ray Chandler_, Aug 25 2015 *)

%Y Cf. A004090, A056570, A216676.

%K nonn,base,easy

%O 0,4

%A _Ravi Bhandari_, Sep 15 2012