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

0,3

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

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

Example

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

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 *)
nxt[{n_, a_}]:={n+1, If[a-1/(n+1)>=0, a-1/(n+1), a+1/(n+1)]}; NestList[nxt, {0, 0}, 40][[;; , 2]]//Denominator (* Harvey P. Dale, Sep 17 2025 *)

Prog

(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
-- Reinhard Zumkeller, Nov 16 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

Crossrefs

Cf. A231692, A005132, A002805, A203811.

Sequence in context: A232090 A203811 A002805 * A375524 A232112 A117481

Adjacent sequences: A231690 A231691 A231692 * A231694 A231695 A231696

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 15 2013

Status

approved