A157699 Decimal expansion of 2*log(1/2 + 1/sqrt(2)).

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

Offset

0,1

Comments

Equals Sum_{n>=1} (-1)^(n+1)*binomial(2n,n)/(n*4^n). A factor 2 is missing in the Lehmer publication.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

D. H. Lehmer, Interesting series involving the Central Binomial Coefficient, Am. Math. Monthly 92, no 7 (1985) 449-457.

Index entries for transcendental numbers

Formula

0.3764528129191954316... = 2*0.1882264064595977158153772035... = 2*log(1.2071067811865...)

Maple

2*log(1/2+1/sqrt(2)) ;

Mathematica

RealDigits[2Log[1/2+1/Sqrt[2]], 10, 120][[1]] (* Harvey P. Dale, Apr 12 2017 *)

Prog

(PARI) default(realprecision, 100); 2*log(1/2+1/sqrt(2)) \\ G. C. Greubel, Oct 02 2018
(Magma) SetDefaultRealField(RealField(100)); 2*Log(1/2+1/Sqrt(2)); // G. C. Greubel, Oct 02 2018

Crossrefs

Sequence in context: A065281 A256848 A019952 * A283270 A159779 A188734

Adjacent sequences: A157696 A157697 A157698 * A157700 A157701 A157702

Keyword

cons,easy,nonn

Author

R. J. Mathar, Mar 04 2009

Status

approved