The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A113479 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A113479

Starting with the fraction 4/1 as the first term, a(n) is the numerator of the reduced fraction of the n-th term according to the rule: if n is even, multiply the previous term by n/(n+1); otherwise multiply the previous term by (n+1)/n.
(history; published version)

#11 by Susanna Cuyler at Thu Jan 14 21:14:46 EST 2021

STATUS

proposed

approved

#10 by Jon E. Schoenfield at Thu Jan 14 21:09:14 EST 2021

STATUS

editing

proposed

#9 by Jon E. Schoenfield at Thu Jan 14 21:09:12 EST 2021

NAME

Starting with the fraction 4/1 as the first term, a(n) is the numerator of the reduced fraction of the n-th term according to the rule: if n is even, multiply the previous term by n/(n+1) ; otherwise multiply the previous term by (n+1)/n.

COMMENTS

The fractions having these numerators slowly converge to Pi. The 1000th term at 2000 digits -digit precision yields 3.1400...

STATUS

approved

editing

#8 by Bruno Berselli at Mon Mar 13 04:29:13 EDT 2017

STATUS

proposed

approved

#7 by Jon E. Schoenfield at Sun Mar 12 18:00:53 EDT 2017

STATUS

editing

proposed

#6 by Jon E. Schoenfield at Sun Mar 12 18:00:49 EDT 2017

COMMENTS

The fractions forming having these numerators slowly converge to Pi. The 1000th term at 2000 digits precision yields 3.1400...

EXAMPLE

The first term is 4/1. then Then the 2nd term is 4/1*2/(2 + 1) = 8/3. So 8 is the 2nd entry in the table.

STATUS

proposed

editing

#5 by G. C. Greubel at Sun Mar 12 17:16:32 EDT 2017

STATUS

editing

proposed

#4 by G. C. Greubel at Sun Mar 12 17:16:23 EDT 2017

LINKS

G. C. Greubel, <a href="/A113479/b113479.txt">Table of n, a(n) for n = 1..1000</a>

MATHEMATICA

a[1] := 4; a[n_] := a[n] = If[EvenQ[n], n*a[n - 1]/(n + 1), (n + 1)*a[n - 1]/n]; Numerator[Table[a[n], {n, 1, 50}]] (* G. C. Greubel, Mar 12 2017 *)

STATUS

approved

editing

#3 by N. J. A. Sloane at Tue Oct 01 17:58:21 EDT 2013

AUTHOR

_Cino Hilliard (hillcino368(AT)gmail.com), _, Jan 09 2006

Discussion

Tue Oct 01

17:58

OEIS Server: https://oeis.org/edit/global/1955

#2 by N. J. A. Sloane at Wed Dec 06 03:00:00 EST 2006

KEYWORD

easy,frac,nonn,new

AUTHOR

Cino Hilliard (hillcino368(AT)hotmailgmail.com), Jan 09 2006