A231693 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).

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

Offset: 0

Author

N. J. A. Sloane, Nov 15 2013

Keywords

• nonn
• frac

Comments

See Comments in A231692, which is the sequence of numerators of {f(n)}.

Note that this sequence is not monotonic.

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

Examples

			0, 1, 1/2, 1/6, 5/12, 13/60, 1/20, 27/140, 19/280, 451/2520, 199/2520, 4709/27720, ...
		

References

• David Wilson, Posting to Sequence Fans Mailing List, Nov 14 2013.

Links

• David W. Wilson, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A231692, A005132, A002805, A203811.

Programs

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
-- Reinhard Zumkeller, Nov 16 2013

Maple

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;

Mathematica

Denominator[FoldList[# + (-1)^Boole[#*#2 >= 1]/#2 &, Range[0, 35]]] (* Paolo Xausa, Aug 16 2025 *)

PARI

s=0;vector(30,n,denominator(s-=(-1)^(n*s<1)/n)) \\ M. F. Hasler, Nov 15 2013

Python

from fractions import Fraction
A231693 = [(f:=Fraction(0)).denominator] + [(f:=(f + (Fraction(1,i) if Fraction(1,i)>f else -Fraction(1,i)))).denominator for i in range(1, 34)]  # Jwalin Bhatt, Apr 08 2025