A145960 Decimal expansion of 2*log(5/3) used in BBP Pi formula.

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

Offset

1,3

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

Index entries for transcendental numbers

Formula

Equals 2*log(5/3) = 2*(log(5)-log(3)) = 2*(A016628 - A002391) = log(25/9) = 4*arctanh(1/4).

Equals Hypergeometric2F1(1, 1/2, 3/2, 1/16).

Equals Sum_{k>=0} (1/16)^k*(1/(2k+1)).

Example

1.021651247531981366411...

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: A358282 A180317 A066654 * A205455 A338135 A350510

Adjacent sequences: A145957 A145958 A145959 * A145961 A145962 A145963

Keyword

cons,nonn

Author

Artur Jasinski, Oct 25 2008

Status

approved