The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. 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:= 4; A215746:= 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.

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