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A269222
Period 4: repeat [1,9,8,9].
0
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.
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
Sequence in context: A157371 A343060 A245330 * A201994 A243277 A200003
KEYWORD
nonn,base,easy
AUTHOR
Peter M. Chema, Jul 11 2016
STATUS
approved