

A096188


Engel expansion of real number x such that y = Gamma(x) is a minimum.


0



1, 3, 3, 7, 13, 14, 14, 27, 27, 46, 99, 549, 913, 2637, 3830, 3929, 15500, 55253, 85854, 246166, 1052057, 2490138, 2521393, 16086534, 29730193, 38774343, 84328391, 317160458, 371478595, 600277187, 811735945, 849656112, 139143919171
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OFFSET

1,2


COMMENTS

Gamma(x) has a minimum at x = 1.46163214496836234126265954232572132846819620400644... (A030169).


LINKS

Table of n, a(n) for n=1..33.
Xavier Gourdon and Pascal Sebah, Some Constants from Number theory from their "Numbers, constants and computation" web site.


MATHEMATICA

EngelExp[ A_, n_ ] := Join[ Array[ 1 &, Floor[ A ]], First@Transpose @ NestList[ {Ceiling[ 1/Expand[ #[[ 1 ]] #[[ 2 ]]  1 ]], Expand[ #[[ 1 ]] #[[ 2 ]]  1]} &, {Ceiling[ 1/(A  Floor[A]) ], A  Floor[A]}, n  1 ]]; EngelExp[ FindMinimum[ Gamma[x], {x, 1, 4}, WorkingPrecision > 2^9][[2, 1, 2]], 32] (* Robert G. Wilson v, Jul 28 2004 *)


CROSSREFS

Cf. A030169.
Sequence in context: A177942 A116880 A051123 * A187873 A306665 A065876
Adjacent sequences: A096185 A096186 A096187 * A096189 A096190 A096191


KEYWORD

nonn


AUTHOR

Gerald McGarvey, Jul 25 2004


EXTENSIONS

Edited and extended by Robert G. Wilson v, Jul 28 2004


STATUS

approved



