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

Author

Artur Jasinski, Oct 25 2008

Keywords

• cons
• nonn

Comments

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

Examples

			1.021651247531981366411...
		

Links

• Eric Weisstein's World of Mathematics, BBP Formula
• Index entries for transcendental numbers

Crossrefs

Cf. A000796, A145961, A145962, A145963.

Programs

Mathematica

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

PARI

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

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)).