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A019774
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Decimal expansion of sqrt(e).
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60
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1, 6, 4, 8, 7, 2, 1, 2, 7, 0, 7, 0, 0, 1, 2, 8, 1, 4, 6, 8, 4, 8, 6, 5, 0, 7, 8, 7, 8, 1, 4, 1, 6, 3, 5, 7, 1, 6, 5, 3, 7, 7, 6, 1, 0, 0, 7, 1, 0, 1, 4, 8, 0, 1, 1, 5, 7, 5, 0, 7, 9, 3, 1, 1, 6, 4, 0, 6, 6, 1, 0, 2, 1, 1, 9, 4, 2, 1, 5, 6, 0, 8, 6, 3, 2, 7, 7, 6, 5, 2, 0, 0, 5, 6, 3, 6, 6, 6, 4
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OFFSET
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1,2
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COMMENTS
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e^(1/2) maximizes the value of x^(c/(x^2)) for any real positive constant c, and minimizes for it for a negative constant, on the range x > 0. - A.H.M. Smeets, Aug 16 2018
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LINKS
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FORMULA
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sqrt(e) = Sum_{n>=0} 1/(2^n*n!) = Sum_{n>=0} 1/(2n)!!. - Daniel Forgues, Apr 17 2011
sqrt(e) = 1 + Sum_{n>0} Product_{i=1..n} 1/(2n). - Ralf Stephan, Sep 11 2013
Continued fraction representation: sqrt(e) = 1 + 1/(1 + 2/(3 + 4/(5 + ... ))). See A000354 for details. - Peter Bala, Jan 30 2015
sqrt(e) = (1/2)*( 1 + (3 + (5 + (7 + ...)/6)/4)/2 ) = 1 + (1 + (1 + (1 + ...)/6)/4)/2. - Rok Cestnik, Jan 19 2017
sqrt(e) = 2*Sum_{n >= 0} 1/((1 - 4*n^2)*(2^n)*n!). - Peter Bala, Jan 16 2022
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EXAMPLE
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1.6487212707001281468486507878141635716537761007101480115750...
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MAPLE
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MATHEMATICA
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PROG
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(PARI) default(realprecision, 20080); x=sqrt(exp(1)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b019774.txt", n, " ", d)); \\ Harry J. Smith, May 01 2009
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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