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A145961 Decimal expansion of 2Log[3] - 4ArcCot[2] = 0.342634... used by BBP Pi formula 4
3, 4, 2, 6, 3, 4, 1, 4, 1, 3, 3, 2, 9, 9, 4, 9, 1, 7, 9, 3, 3, 4, 6, 5, 5, 4, 8, 0, 0, 0, 1, 9, 3, 8, 0, 1, 1, 8, 0, 8, 3, 2, 8, 9, 8, 5, 0, 1, 0, 1, 7, 8, 4, 8, 2, 2, 5, 6, 5, 6, 3, 1, 2, 3, 9, 4, 1, 9, 7, 1, 2, 9, 7, 7, 4, 2, 5, 1, 1, 1, 2, 5, 4, 4, 8, 3, 0, 3, 7, 3, 6, 8, 7, 9, 1, 2, 6, 0, 7, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A145961 = 2Log[3] - 4ArcCot[2] =

1/3 Hypergeometric2F1[1, 3/4, 7/4, 1/16] =

Sum[(1/16)^n (1/(4n+3)),{n,0,Infinity}]

BBP Formula on Pi = 4*A145963-(1/2)A145960-(1/2)A145961-A145962 =

(*Artur Jasinski*) =4((1/16) (Pi + 4 ArcTan[1/3] + 4 Sqrt[2] ArcTan[1/Sqrt[2]] + Log[25] - 2 Sqrt[2] Log[2 - Sqrt[2]] + 2 Sqrt[2] Log[2 + Sqrt[2]]))-

(Sqrt[2] ArcCot[Sqrt[2]] + Sqrt[2] ArcCoth[Sqrt[2]] - Log[5]/2 - Pi/4 - ArcCot[3])-

(1/2)(2*Log[5/3])-

(1/2)(2*Log[3]-2 ArcTan[1/2]) =

Pi = 3.1414... = A000796

LINKS

Table of n, a(n) for n=0..99.

Weisstein, Eric W., BBP Formula.

MATHEMATICA

k=First[RealDigits[2Log[3] - 4ArcCot[2], 10, 100]]; Prepend[k, 0]

CROSSREFS

A000796, A145961, A145962, A145963

Sequence in context: A133620 A322965 A154570 * A082928 A139524 A247413

Adjacent sequences:  A145958 A145959 A145960 * A145962 A145963 A145964

KEYWORD

cons,nonn

AUTHOR

Artur Jasinski, Oct 25 2008

EXTENSIONS

Removed leading zero, adjusted offset R. J. Mathar, Feb 05 2009

STATUS

approved

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Last modified September 15 16:12 EDT 2019. Contains 327078 sequences. (Running on oeis4.)