A269222 Period 4: repeat [1,9,8,9].

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

Offset

1,2

Comments

Digital root of Fib(18*n).

Decimal expansion of 221/1111.

Links

Table of n, a(n) for n=1..88.

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

Formula

a(n) = A010888(Fibonacci(18*n)).

From Wesley Ivan Hurt, Sep 03 2022: (Start)

a(n) = a(n-4) for n >= 5.

a(n) = (9/4)*(3+(-1)^n)-7*sin(n*Pi/2)/2. (End)

Example

For n=2, a(2) = digital root of Fibonacci(18*2) or 14930352; therefore, a(2) = 9, since the digital root of 14930352 = 9.

Mathematica

Table[NestWhile[Total@ IntegerDigits@ # &, Fibonacci[18 n], IntegerLength@ # > 1 &], {n, 120}] (* Michael De Vlieger, Jul 11 2016 *)
PadRight[{}, 100, {1, 9, 8, 9}] (* Harvey P. Dale, Sep 24 2021 *)

Prog

(PARI) a(n)=[9, 1, 9, 8][n%4+1] \\ Charles R Greathouse IV, Jul 21 2016

Crossrefs

Cf. A008600, A010888.

Sequence in context: A157371 A343060 A245330 * A201994 A243277 A200003

Adjacent sequences: A269219 A269220 A269221 * A269223 A269224 A269225

Keyword

nonn,base,easy

Author

Peter M. Chema, Jul 11 2016

Status

approved