A216754 Digital root of fourth power of Fibonacci numbers.

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

Author

Ravi Bhandari, Sep 15 2012

Keywords

• nonn
• base
• easy

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, ...

Links

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

Crossrefs

Cf. A004090, A216676, A216699.

Programs

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 *)

Extensions

Extended by Ray Chandler, Aug 27 2015