A059514 For a rational number p/q let f(p/q) = p*q divided by (the sum of digits of p and of q) minus 1; a(n) is obtained by iterating f, starting at n/1, until an integer is reached, or if no integer is ever reached then a(n) = 0.

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 11, 4, 28, 42, 7315, 208, 136, 2, 19, 10, 7, 11, 69, 4, 2310, 28, 3, 42, 319, 10, 189885850, 96, 11, 323323, 205530, 4, 37, 228, 28, 10, 123, 7, 559, 11, 5, 69, 517, 4, 152152, 10, 187, 28, 424, 6, 11, 154, 0, 77140, 2478, 10, 0

Offset: 1

Author

Floor van Lamoen, Jan 22 2001

Keywords

• base
• easy
• nonn

Comments

a(A216183(n)) = 0. - Reinhard Zumkeller, Mar 11 2013

Examples

			14/1 -> 14/5 -> 70/9 -> 630/15 = 42 so a(14)=42.
57/1 -> 19/4 -> 76/13 -> 247/4 -> 247/4 -> ...  so a(57) = 0.
		

Links

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

Crossrefs

Cf. A059175, A058971, A058972, A058977, A058988.

Cf. A007953.

Programs

Haskell

import Data.Ratio ((%), numerator, denominator)
a059514 n = f [n % 1] where
   f xs@(x:_)
     | denominator y == 1 = numerator y
     | y `elem` xs        = 0
     | otherwise          = f (y : xs)
     where y = (numerator x * denominator x) %
               (a007953 (numerator x) + a007953 (denominator x) - 1)
-- Reinhard Zumkeller, Mar 11 2013

Extensions

Corrected and extended by Naohiro Nomoto, Jul 20 2001