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A059514
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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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2
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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
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OFFSET
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1,10
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COMMENTS
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LINKS
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EXAMPLE
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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.
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PROG
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(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)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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