login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A215746 Numerator of sum(i=0..n, (-1)^i*4/(2*i + 1)). 1
4, 8, 52, 304, 1052, 10312, 147916, 135904, 2490548, 44257352, 47028692, 1023461776, 5385020324, 15411418072, 467009482388, 13895021563328, 14442004718228, 13926277743608, 533322720625196, 516197940314096, 21831981985010836, 911392701638017048, 937558224301357108 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Denominator of the sum divides A025547(n+1), but is not always equal to it: the first exception is  n = 32.

x(n) = sum(i=0..n, (-1)^i*4/(2*i+1)) very slowly converges to Pi, with x(n) > Pi when n is even and x(n) < Pi when n is odd.

LINKS

Robert Israel, Table of n, a(n) for n = 0..229

Eric W. Weisstein, MathWorld: Pi formulas

EXAMPLE

a(2) = 52 because 4 - 4/3 + 4/5 = 60/15 - 20/15 + 12/15 = 52/15.

MAPLE

N:= 100; # to get terms up to a[N]

T[0]:= 4;

A215746[0]:= 4;

for i from 1 to N do

  T[i]:= T[i-1] + (-1)^i*4/(2*i+1);

  A215746[i]:= numer(T[i])

od:

[seq](A215746[i], i=0..N); # Robert Israel, Apr 27 2014

MATHEMATICA

Table[Numerator[Sum[(-1)^i 4/(2i + 1), {i, 0, n}]], {n, 0, 39}]

CROSSREFS

Cf. A007509.

Sequence in context: A329942 A056397 A189314 * A128893 A214603 A192508

Adjacent sequences:  A215743 A215744 A215745 * A215747 A215748 A215749

KEYWORD

nonn,easy,frac

AUTHOR

Alonso del Arte, Aug 22 2012

EXTENSIONS

Definition and comments corrected by Robert Israel, Apr 27 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 25 00:34 EDT 2021. Contains 345445 sequences. (Running on oeis4.)