A216699 Digital root of cubes of Fibonacci numbers.

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, 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, 9, 8, 8, 1, 9, 1, 1, 8, 9, 8, 8, 1, 9, 1, 1, 8, 9, 8, 8

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..86.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).

Mathematica

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

Crossrefs

Cf. A004090, A056570, A216676.

Sequence in context: A356532 A019873 A274330 * A011010 A019606 A010732

Adjacent sequences: A216696 A216697 A216698 * A216700 A216701 A216702

Keyword

nonn,base,easy

Author

Ravi Bhandari, Sep 15 2012

Status

approved