%I #24 Nov 16 2013 11:03:42
%S 1,1,2,6,12,60,20,140,280,2520,2520,27720,27720,360360,360360,360360,
%T 720720,12252240,4084080,77597520,77597520,11085360,11085360,
%U 254963280,84987760,424938800,424938800,11473347600,80313433200,2329089562800,2329089562800,72201776446800,144403552893600,144403552893600
%N 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).
%C See Comments in A231692, which is the sequence of numerators of {f(n)}.
%C Note that this sequence is not monotonic.
%C Differs from A002805 starting at a(20)=77597520: A002805(20)=15519504. See also A203811 for a very similar idea. - _M. F. Hasler_, Nov 15 2013
%D David Wilson, Posting to Sequence Fans Mailing List, Nov 14 2013.
%H David W. Wilson, <a href="/A231693/b231693.txt">Table of n, a(n) for n = 0..200</a>
%e 0, 1, 1/2, 1/6, 5/12, 13/60, 1/20, 27/140, 19/280, 451/2520, 199/2520, 4709/27720, ...
%p f:=proc(n) option remember;
%p if n=0 then 0 elif
%p f(n-1) >= 1/n then f(n-1)-1/n else f(n-1)+1/n; fi; end;
%o (PARI) s=0;vector(30,n,denominator(s-=(-1)^(n*s<1)/n)) \\ - _M. F. Hasler_, Nov 15 2013
%o (Haskell)
%o a231693 n = a231693_list !! n
%o a231693_list = map denominator $ 0 : wilson 1 0 where
%o wilson x y = y' : wilson (x + 1) y'
%o where y' = y + (if y < 1 % x then 1 else -1) % x
%o -- _Reinhard Zumkeller_, Nov 16 2013
%Y Cf. A231692, A005132, A002805, A203811.
%K nonn,frac
%O 0,3
%A _N. J. A. Sloane_, Nov 15 2013