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%I #4 Sep 17 2014 19:00:18
%S 1,1,1,1,2,1,1,1,2,1,2,1,2,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,2,1,
%T 2,1,2,1,2,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1,1,2,1,2,1,
%U 2,1,2,1,2,1,2,1,1,1,2,1,2,1,1,1,2,1
%N Number of iterations needed in A058977 to reach a result.
%C a(A247468(n)) = n and a(m) < n for m < A247468(n).
%H Reinhard Zumkeller, <a href="/A247462/b247462.txt">Table of n, a(n) for n = 1..10000</a>
%e Consider f-trajectories and their lengths, where f(p/q)=A008472(p+q)/A001221(p+q), the iterating function in definition of A058977:
%e a(454) = 3: 454/1 - 25/3 - 9/2 - 11/1
%e a(1401) = 4: 1401/1 - 703/2 - 55/3 - 31/2 - 7/1;
%e a(7364) = 5: 7364/1 - 499/3 - 253/2 - 25/3 - 9/2 - 11/1.
%o (Haskell)
%o import Data.Ratio ((%), numerator, denominator, Ratio)
%o a247462 1 = 1
%o a247462 n = fst $ until ((== 1) . denominator . snd)
%o (\(i, x) -> (i + 1, f x)) (0, 1 % n) where
%o f x = a008472 x' % a001221 x' where x' = numerator x + denominator x
%Y Cf. A058977, A008472, A001221, A247468.
%K nonn
%O 1,5
%A _Reinhard Zumkeller_, Sep 17 2014
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