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Search: id:A145960
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| A145960 |
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Decimal expansion of 2*Log[5/3] = 1.0216... used by BBP Pi formula |
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+0
4
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| 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; cons; graph; listen)
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OFFSET
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1,3
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COMMENT
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A145960 = 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
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LINKS
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Weisstein, Eric W., BBP Formula.
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MAPLE
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First[RealDigits[2 Log[5/3], 10, 100]]
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CROSSREFS
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A000796, A145961, A145962, A145963
Sequence in context: A128728 A084950 A066654 this_sequence A108767 A046817 A008970
Adjacent sequences: A145957 A145958 A145959 this_sequence A145961 A145962 A145963
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KEYWORD
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cons,nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Oct 25 2008
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