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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.
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%I #7 Mar 02 2015 16:08:45

%S 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,

%T 28,3,42,319,10,189885850,96,11,323323,205530,4,37,228,28,10,123,7,

%U 559,11,5,69,517,4,152152,10,187,28,424,6,11,154,0,77140,2478,10,0

%N 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.

%C a(A216183(n)) = 0. - _Reinhard Zumkeller_, Mar 11 2013

%H Reinhard Zumkeller, <a href="/A059514/b059514.txt">Table of n, a(n) for n = 1..10000</a>

%e 14/1 -> 14/5 -> 70/9 -> 630/15 = 42 so a(14)=42.

%e 57/1 -> 19/4 -> 76/13 -> 247/4 -> 247/4 -> ... so a(57) = 0.

%o (Haskell)

%o import Data.Ratio ((%), numerator, denominator)

%o a059514 n = f [n % 1] where

%o f xs@(x:_)

%o | denominator y == 1 = numerator y

%o | y `elem` xs = 0

%o | otherwise = f (y : xs)

%o where y = (numerator x * denominator x) %

%o (a007953 (numerator x) + a007953 (denominator x) - 1)

%o -- _Reinhard Zumkeller_, Mar 11 2013

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

%Y Cf. A007953.

%K base,easy,nonn

%O 1,10

%A _Floor van Lamoen_, Jan 22 2001

%E Corrected and extended by _Naohiro Nomoto_, Jul 20 2001