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A145960 Decimal expansion of 2*Log[5/3] = 1.0216... used by BBP Pi formula 4
1, 0, 2, 1, 6, 5, 1, 2, 4, 7, 5, 3, 1, 9, 8, 1, 3, 6, 6, 4, 1, 1, 0, 2, 8, 1, 9, 2, 6, 0, 7, 3, 2, 3, 8, 6, 9, 7, 5, 6, 2, 2, 1, 5, 9, 2, 8, 9, 1, 5, 3, 6, 5, 4, 0, 3, 5, 5, 9, 0, 7, 1, 1, 5, 6, 7, 3, 3, 6, 9, 3, 8, 8, 9, 7, 8, 0, 9, 7, 5, 9, 5, 5, 1, 3, 0, 3, 6, 2, 4, 6, 5, 5, 8, 8, 9, 5, 0, 4, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equals 2*Log[5/3] = 2(Log[5]-Log[3]) = Log[25/9] = 4 ArcTanh[1/4] =

Hypergeometric2F1[1, 1/2, 3/2, 1/16] = Sum[(1/16)^n (1/(2n+1)),{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=1..100.

Eric W. Weisstein, BBP Formula

MATHEMATICA

First[RealDigits[2 Log[5/3], 10, 100]]

PROG

(PARI) 2*log(5/3) \\ Michel Marcus, Apr 05 2015

CROSSREFS

Cf. A000796, A145961, A145962, A145963.

Sequence in context: A084950 A180317 A066654 * A205455 A259332 A108767

Adjacent sequences:  A145957 A145958 A145959 * A145961 A145962 A145963

KEYWORD

cons,nonn

AUTHOR

Artur Jasinski, Oct 25 2008

STATUS

approved

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Last modified May 23 23:53 EDT 2017. Contains 286937 sequences.