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A131920 Decimal expansion of 2/log(2). 1
2, 8, 8, 5, 3, 9, 0, 0, 8, 1, 7, 7, 7, 9, 2, 6, 8, 1, 4, 7, 1, 9, 8, 4, 9, 3, 6, 2, 0, 0, 3, 7, 8, 4, 2, 7, 4, 8, 5, 3, 2, 9, 1, 9, 0, 8, 3, 0, 5, 9, 7, 1, 8, 6, 8, 2, 7, 0, 8, 9, 8, 8, 1, 3, 8, 6, 2, 2, 1, 8, 4, 3, 8, 3, 6, 2, 3, 7, 0, 1, 5, 9, 7, 7, 1, 0, 5, 3, 2, 4, 5, 7, 8, 7, 0, 1, 2, 6, 8, 8, 9, 9, 3, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Arises in maximal arithmetic progressions in random subsets.

Benjamini et al. use this constant as follows: "Let U(N) denote the maximal length of arithmetic progressions in a random uniform subset of {0, 1}^N. By an application of the Chen-Stein method, we show that U(N) - 2 log(N)/log(2) converges in law to an extreme type (asymmetric) distribution. The same result holds for the maximal length W(N) of arithmetic progressions (mod N). When considered in the natural way on a common probability space, we observe that U(N)/log(N) converges almost surely to 2/log(2), while W(N)/log(N) does not converge almost surely (and in particular, limsup W(N)/log(N) is at least 3/log(2))."

LINKS

Table of n, a(n) for n=1..105.

Itai Benjamini, Ariel Yadin and Ofer Zeitouni, Maximal Arithmetic Progressions in Random Subsets

Index entries for transcendental numbers

FORMULA

The continued fraction expansion is: 2 + 1/1 + 1/7 + 1/1 + 1/2 + 1/1 + 1/1 + 1/1 + 1/3 + 1/2 + 1/4 + 1/7 + 1/5 + 1/3 + 1/6 + 1/4 + 1/1 + 1/1 + 1/4 + 1/1 + 1/1 + 1/27 + 1/3 + 1/1 + 1/1 + 1/1 + 1/1 + 1/4 + 1/1 + 1/3 + 1/4 + 1/2 + 1/3 + 1/2 + 1/1 + 1/2 + 1/29 + 1/1 + 1/4 + 1/1 + 1/9 + 1/1 + 1/36 + 1/1 + 1/1 + 1/10 + 1/1 + 1/2 + 1/1 + 1/2 + 1/1 + 1/3 + 1/6 + 1/1 + 1/1 + 1/27 + 1/1 + 1/1 + 1/9 + 1/2 + 1/2 + 1/1 + 1/1 + 1/4 + 1/5 + 1/8 + 1/1 + 1/1 + 1/1 + 1/2 + 1/1 + 1/65 + 1/4 + 1/1 + 1/1 + 1/2 + 1/2 + 1/11 + 1/10 + 1/1 + 1/1 + 1/18 + 1/4 + 1/3 + 1/1 + 1/3 + 1/3 + 1/4 + 1/3 + 1/2 + 1/10 + 1/2 + 1/65 + 1/1 + 1/9 + 1/5 + 1/105 + 1/21 + 1/1 + 1/3 + ...

2/log(2) = 1/log(32) = 1/(5log(2)). - Alonso del Arte, Feb 01 2015

EXAMPLE

2/log(2) = 2.885390081777926814719849362...

MATHEMATICA

RealDigits[2/Log[2], 10, 128][[1]] (* Alonso del Arte, Feb 01 2015 *)

PROG

(PARI) 2/log(2) \\ Charles R Greathouse IV, Feb 02 2015

CROSSREFS

Cf. A002162.

Sequence in context: A198234 A197385 A010596 * A180308 A155739 A197139

Adjacent sequences:  A131917 A131918 A131919 * A131921 A131922 A131923

KEYWORD

cons,easy,nonn

AUTHOR

Jonathan Vos Post, Jul 28 2007

STATUS

approved

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)