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

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, 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, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1

Offset: 1

Author

Reinhard Zumkeller, Sep 17 2014

Keywords

• nonn

Comments

a(A247468(n)) = n and a(m) < n for m < A247468(n).

Examples

			Consider f-trajectories and their lengths, where f(p/q)=A008472(p+q)/A001221(p+q), the iterating function in definition of A058977:
a(454) = 3: 454/1 - 25/3 - 9/2 - 11/1
a(1401) = 4: 1401/1 - 703/2 - 55/3 - 31/2 - 7/1;
a(7364) = 5: 7364/1 - 499/3 - 253/2 - 25/3 - 9/2 - 11/1.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A058977, A008472, A001221, A247468.

Programs

Haskell

import Data.Ratio ((%), numerator, denominator, Ratio)
a247462 1 = 1
a247462 n = fst $ until ((== 1) . denominator . snd)
                        (\(i, x) -> (i + 1, f x)) (0, 1 % n) where
   f x = a008472 x' % a001221 x' where x' = numerator x + denominator x