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A081478
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Consider the mapping f(a/b) = (a - b)/(ab). Taking a = 2 and b = 1 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 2/1,1/2,-1/2,-3/-2,-1/6,... Sequence contains the denominators.
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2
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1, 2, 2, -2, 6, -6, 42, -42, 1806, -1806, 3263442, -3263442, 10650056950806, -10650056950806, 113423713055421844361000442, -113423713055421844361000442, 12864938683278671740537145998360961546653259485195806
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OFFSET
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1,2
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COMMENTS
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The mapping f(a/b) = (a + b)/(a - b). Taking a = 2 and b = 1 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the periodic sequence 2/1,3/1,2/1,3/1,...
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LINKS
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FORMULA
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MATHEMATICA
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Last /@ NestList[{(#1 - #2), #1 #2} & @@ # &, {2, 1}, 16] (* Michael De Vlieger, Sep 04 2016 *)
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PROG
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(Sage)
# Variant with first four terms slightly different. Absolute values.
x, y = 1, 2
yield x
while True:
yield x
x, y = x * y, x//y + 1
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003
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STATUS
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approved
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