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A092042
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Decimal expansion of e^(1/4).
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4
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1, 2, 8, 4, 0, 2, 5, 4, 1, 6, 6, 8, 7, 7, 4, 1, 4, 8, 4, 0, 7, 3, 4, 2, 0, 5, 6, 8, 0, 6, 2, 4, 3, 6, 4, 5, 8, 3, 3, 6, 2, 8, 0, 8, 6, 5, 2, 8, 1, 4, 6, 3, 0, 8, 9, 2, 1, 7, 5, 0, 7, 2, 9, 6, 8, 7, 2, 2, 0, 7, 7, 6, 5, 8, 6, 7, 2, 3, 8, 0, 0, 2, 7, 5, 3, 3, 0, 6, 4, 1, 9, 4, 3, 9, 5, 5, 3, 5, 6, 8
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OFFSET
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1,2
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COMMENTS
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e^(1/4) is also the integral from 0 to infinity of e^(-x) * I_0(sqrt(x)), where I_0(z) is a modified Bessel function. - Jean-François Alcover, Mar 10 2011
e^(1/4) maximizes the value of x^(c/(x^4)) 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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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
D. M. Bătinetu-Giurgiu, Problem 4133, Crux Mathematicorum, Vol. 42, No. 4 (2016), p. 174; Solution to Problem 4133, ibid., Vol. 43, No. 4 (2017), pp. 167-169.
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FORMULA
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e^(1/4) = 1/2*( 1 +(5 +(9 +(13 +...)/12)/8)/4 ) = 1 +(1 +(1 +(1 +...)/12)/8)/4. - Rok Cestnik, Jan 19 2017
Equals lim_{n->oo} ((2*n-1)!!)^(1/(2*n))/A057863(n)^(1/n^2) (Bătinetu-Giurgiu, 2016). - Amiram Eldar, Apr 10 2022
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EXAMPLE
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1.28402541668774148407342056806243645833... - Muniru A Asiru, Aug 16 2018
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MAPLE
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evalf(exp(1/4)); # Muniru A Asiru, Aug 16 2018
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MATHEMATICA
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RealDigits[(E)^(1/4), 10, 100][[1]] (* Vincenzo Librandi, Mar 01 2013 *)
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PROG
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(PARI) exp(1/4) \\ Michel Marcus, Jan 19 2017
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CROSSREFS
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Cf. A001113, A019774, A057863, A078688, A092426.
Sequence in context: A268491 A076588 A068565 * A158934 A021356 A030345
Adjacent sequences: A092039 A092040 A092041 * A092043 A092044 A092045
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KEYWORD
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cons,nonn
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AUTHOR
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Mohammad K. Azarian, Mar 27 2004
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STATUS
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approved
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