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A231693
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Define a sequence of rationals by f(0)=0, thereafter f(n)=f(n-1)-1/n if that is >= 0, otherwise f(n)=f(n-1)+1/n; a(n) = denominator of f(n).
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3
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1, 1, 2, 6, 12, 60, 20, 140, 280, 2520, 2520, 27720, 27720, 360360, 360360, 360360, 720720, 12252240, 4084080, 77597520, 77597520, 11085360, 11085360, 254963280, 84987760, 424938800, 424938800, 11473347600, 80313433200, 2329089562800, 2329089562800, 72201776446800, 144403552893600, 144403552893600
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OFFSET
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0,3
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COMMENTS
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See Comments in A231692, which is the sequence of numerators of {f(n)}.
Note that this sequence is not monotonic.
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REFERENCES
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David Wilson, Posting to Sequence Fans Mailing List, Nov 14 2013.
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LINKS
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EXAMPLE
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0, 1, 1/2, 1/6, 5/12, 13/60, 1/20, 27/140, 19/280, 451/2520, 199/2520, 4709/27720, ...
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MAPLE
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f:=proc(n) option remember;
if n=0 then 0 elif
f(n-1) >= 1/n then f(n-1)-1/n else f(n-1)+1/n; fi; end;
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PROG
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(PARI) s=0; vector(30, n, denominator(s-=(-1)^(n*s<1)/n)) \\ - M. F. Hasler, Nov 15 2013
(Haskell)
a231693 n = a231693_list !! n
a231693_list = map denominator $ 0 : wilson 1 0 where
wilson x y = y' : wilson (x + 1) y'
where y' = y + (if y < 1 % x then 1 else -1) % x
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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