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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). 3
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 (list; graph; refs; listen; history; text; internal format)
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;

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

CROSSREFS

Cf. A231692, A005132, A002805, A203811.

Sequence in context: A232090 A203811 A002805 * A232112 A117481 A343277

Adjacent sequences:  A231690 A231691 A231692 * A231694 A231695 A231696

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Nov 15 2013

STATUS

approved

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Last modified May 23 14:00 EDT 2022. Contains 353975 sequences. (Running on oeis4.)