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Search: id:A131920
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| A131920 |
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Decimal expansion of 2/ln(2). Arises in maximal arithmetic progressions in random subsets. |
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+0
1
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| 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; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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2.88539008.... Benajmini 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))."
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LINKS
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Itai Benjamini, Ariel Yadin and Ofer Zeitouni, Maximal Arithmetic Progressions in Random Subsets
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FORMULA
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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 + . . .
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CROSSREFS
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Cf. A002162.
Sequence in context: A011061 A011288 A010596 this_sequence A155739 A021780 A020769
Adjacent sequences: A131917 A131918 A131919 this_sequence A131921 A131922 A131923
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 28 2007
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