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A247462 Number of iterations needed in A058977 to reach a result.

%I A247462 #4 Sep 17 2014 19:00:18
%S A247462 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 A247462 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 A247462 2,1,2,1,2,1,2,1,1,1,2,1,2,1,1,1,2,1
%N A247462 Number of iterations needed in A058977 to reach a result.
%C A247462 a(A247468(n)) = n and a(m) < n for m < A247468(n).
%H A247462 Reinhard Zumkeller, <a href="/A247462/b247462.txt">Table of n, a(n) for n = 1..10000</a>
%e A247462 Consider f-trajectories and their lengths, where f(p/q)=A008472(p+q)/A001221(p+q), the iterating function in definition of A058977:
%e A247462 a(454) = 3: 454/1 - 25/3 - 9/2 - 11/1
%e A247462 a(1401) = 4: 1401/1 - 703/2 - 55/3 - 31/2 - 7/1;
%e A247462 a(7364) = 5: 7364/1 - 499/3 - 253/2 - 25/3 - 9/2 - 11/1.
%o A247462 (Haskell)
%o A247462 import Data.Ratio ((%), numerator, denominator, Ratio)
%o A247462 a247462 1 = 1
%o A247462 a247462 n = fst $ until ((== 1) . denominator . snd)
%o A247462                         (\(i, x) -> (i + 1, f x)) (0, 1 % n) where
%o A247462    f x = a008472 x' % a001221 x' where x' = numerator x + denominator x
%Y A247462 Cf. A058977, A008472, A001221, A247468.
%K A247462 nonn
%O A247462 1,5
%A A247462 _Reinhard Zumkeller_, Sep 17 2014