The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A132049 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A132049

Numerator of 2*n*A000111(n-1)/A000111(n): approximations of Pi, using Euler (up/down) numbers.
(history; published version)

#45 by Peter Luschny at Sat Jun 11 11:43:14 EDT 2022

STATUS

proposed

approved

#44 by Michel Marcus at Sat Jun 11 10:12:13 EDT 2022

STATUS

editing

proposed

#43 by Michel Marcus at Sat Jun 11 10:12:04 EDT 2022

LINKS

Leonhard Euler, <a href="http://arxiv.org/abs/math/0506415">On the sums of series of reciprocals, </a>, (Presented to the St. Petersburg Academy on December 5, 1735), last paragraph, <a href="http://arxiv.org/abs/math/0506415v2">arXiv:math/0506415v2</a> 0506415 [math.HO]. [Peter Luschny, Nov 18 , 2005-2008].

STATUS

proposed

editing

#42 by Chai Wah Wu at Sat Jun 11 10:09:02 EDT 2022

STATUS

editing

proposed

#41 by Chai Wah Wu at Sat Jun 11 10:08:58 EDT 2022

PROG

blist = (0, 1, )

yield Fraction(2*n*sum(blist), sum[-1], (blist:=tuple(accumulate(reversed(blist), initial=0)))[-1]).numerator

A132049_list = list(islice(A132049_gen(), 40)) # Chai Wah Wu, Jun 09 -11 2022

STATUS

approved

editing

#40 by Alois P. Heinz at Thu Jun 09 20:13:14 EDT 2022

STATUS

proposed

approved

#39 by Chai Wah Wu at Thu Jun 09 19:45:29 EDT 2022

STATUS

editing

proposed

#38 by Chai Wah Wu at Thu Jun 09 19:45:18 EDT 2022

PROG

(Python)

from itertools import islice, count, accumulate

from fractions import Fraction

def A132049_gen(): # generator of terms

yield 2

blist = (1, )

for n in count(2):

yield Fraction(2*n*sum(blist), sum(blist:=tuple(accumulate(reversed(blist), initial=0)))).numerator

A132049_list = list(islice(A132049_gen(), 40)) # Chai Wah Wu, Jun 09 2022

STATUS

approved

editing

#37 by Susanna Cuyler at Sun Feb 25 22:55:53 EST 2018

STATUS

proposed

approved

#36 by Jon E. Schoenfield at Sun Feb 25 22:29:00 EST 2018

STATUS

editing

proposed