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Search: id:A002162
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| A002162 |
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Decimal expansion of natural logarithm of 2.
(Formerly M4074 N1689)
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+0
10
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| 6, 9, 3, 1, 4, 7, 1, 8, 0, 5, 5, 9, 9, 4, 5, 3, 0, 9, 4, 1, 7, 2, 3, 2, 1, 2, 1, 4, 5, 8, 1, 7, 6, 5, 6, 8, 0, 7, 5, 5, 0, 0, 1, 3, 4, 3, 6, 0, 2, 5, 5, 2, 5, 4, 1, 2, 0, 6, 8, 0, 0, 0, 9, 4, 9, 3, 3, 9, 3, 6, 2, 1, 9, 6, 9, 6, 9, 4, 7, 1, 5, 6, 0, 5, 8, 6, 3, 3, 2, 6, 9, 9, 6, 4, 1, 8, 6, 8, 7
(list; cons; graph; listen)
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OFFSET
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0,1
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.3.3.
D. W. Sweeney, On the computation of Euler's constant, Math. Comp., 17 (1963), 170-178.
Uhler, Horace S.; Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7 and 17. Proc. Nat. Acad. Sci. U. S. A. 26, (1940). 205-212.
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LINKS
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D. H. Bailey and J. M. Borwein, Experimental Mathematics: Examples, Methods and Implications
X. Gourdon and P. Sebah, The logarithm constant:log(2)
S. Plouffe, log(2), natural logarithm of 2 to 2000 places
S. Ramanujan, Question 260, J. Ind. Math. Soc.
Eric Weisstein's World of Mathematics, Natural Logarithm of 2
Eric Weisstein's World of Mathematics, Masser-Gramain Constant
Eric Weisstein's World of Mathematics, Logarithmic Integral
Paul Cooijmans, Odds.
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FORMULA
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log(2) = Sum_{ k >= 1 } 1/(k*2^k) = Sum_{j >= 1} (-1)^(j+1)/j.
log(2) = Integral_{t = 0..1 } dt/(1+t).
log(2) = 2/3 * (1 + Sum{k=1..inf, 2/[(4k)^3-4k]}) (Ramanujan).
log(2)=4*sum_{k=0..inf} [3-2*sqrt(2)]^(2k+1)/(2k+1) (Y. Luke) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 13 2006
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EXAMPLE
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.6931471805599453...
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CROSSREFS
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Sequence in context: A129938 A022698 A013707 this_sequence A072365 A085138 A021148
Adjacent sequences: A002159 A002160 A002161 this_sequence A002163 A002164 A002165
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KEYWORD
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cons,nonn
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AUTHOR
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njas
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