login
A216754
Digital root of fourth power of Fibonacci numbers.
0
0, 1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9, 1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9, 1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9, 1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9, 1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9, 1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9, 1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9, 1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9, 1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9
OFFSET
0,4
COMMENTS
This sequence is periodic with period 12. Also, the first (2n - 1) terms are symmetric about n-th term, where n = 6k, k = 1, 2, 3, ...
MATHEMATICA
Table[NestWhile[Total[IntegerDigits[#]] &, Fibonacci[n]^4, # > 9 &], {n, 0, 86}] (* T. D. Noe, Oct 15 2012 *)
Join[{0}, LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 7, 9, 4, 1, 4, 9, 7, 1, 1, 9}, 108]] (* Ray Chandler, Aug 27 2015 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Ravi Bhandari, Sep 15 2012
EXTENSIONS
Extended by Ray Chandler, Aug 27 2015
STATUS
approved