A145963 Decimal expansion of Hypergeometric2F1[1, 1/8, 9/8, 1/16] used in BBP Pi formula.

1, 0, 0, 7, 1, 8, 4, 4, 7, 6, 4, 1, 4, 6, 7, 6, 2, 2, 8, 6, 4, 4, 7, 6, 0, 1, 4, 7, 4, 5, 0, 4, 3, 8, 4, 9, 6, 6, 4, 2, 9, 6, 5, 4, 7, 1, 9, 4, 5, 8, 8, 3, 1, 1, 3, 7, 1, 6, 4, 3, 6, 2, 0, 3, 1, 7, 2, 3, 5, 2, 3, 9, 0, 3, 8, 0, 8, 9, 8, 1, 6, 3, 5, 2, 7, 8, 6, 8, 9, 4, 4, 2, 8, 9, 5, 8, 5, 9, 4, 9

Offset

1,4

Comments

BBP formula for Pi = 4*A145963 - (1/2)*A145960 - (1/2)*A145961 - A145962.

Links

Table of n, a(n) for n=1..100.

Eric Weisstein's World of Mathematics, BBP Formula.

Formula

Equals Sum_{k>=0} (1/16)^k / (8*k+1).

Example

1.00718447641467622864476...

Mathematica

First[RealDigits[Hypergeometric2F1[1, 1/8, 9/8, 1/16], 10, 100]]
N[(1/16) (Pi + 2 Sqrt[2] (2 ArcCoth[Sqrt[2]] + ArcTan[2 Sqrt[2]]) + 2 ArcTan[3/4] + 2 Log[5]), 100]
N[Sum[(1/16)^n (1/(8n+1)), {n, 0, Infinity}], 100]

Prog

(PARI) suminf(k=0, (1/16)^k / (8*k+1)) \\ Michel Marcus, Jan 16 2021

Crossrefs

Cf. A000796, A145960, A145961, A145962.

Sequence in context: A021586 A091131 A249279 * A199439 A153625 A011100

Adjacent sequences: A145960 A145961 A145962 * A145964 A145965 A145966

Keyword

cons,nonn

Author

Artur Jasinski, Oct 25 2008

Status

approved