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%I #26 Sep 03 2022 23:41:30
%S 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,
%T 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,
%U 1,9,8,9,1,9,8,9,1,9,8,9,1,9,8,9,1,9,8,9
%N Period 4: repeat [1,9,8,9].
%C Digital root of Fib(18*n).
%C Decimal expansion of 221/1111.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F a(n) = A010888(Fibonacci(18*n)).
%F From _Wesley Ivan Hurt_, Sep 03 2022: (Start)
%F a(n) = a(n-4) for n >= 5.
%F a(n) = (9/4)*(3+(-1)^n)-7*sin(n*Pi/2)/2. (End)
%e For n=2, a(2) = digital root of Fibonacci(18*2) or 14930352; therefore, a(2) = 9, since the digital root of 14930352 = 9.
%t Table[NestWhile[Total@ IntegerDigits@ # &, Fibonacci[18 n], IntegerLength@ # > 1 &], {n, 120}] (* _Michael De Vlieger_, Jul 11 2016 *)
%t PadRight[{},100,{1,9,8,9}] (* _Harvey P. Dale_, Sep 24 2021 *)
%o (PARI) a(n)=[9,1,9,8][n%4+1] \\ _Charles R Greathouse IV_, Jul 21 2016
%Y Cf. A008600, A010888.
%K nonn,base,easy
%O 1,2
%A _Peter M. Chema_, Jul 11 2016
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