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%I #5 Mar 28 2015 18:13:15
%S 1,3,3,7,13,14,14,27,27,46,99,549,913,2637,3830,3929,15500,55253,
%T 85854,246166,1052057,2490138,2521393,16086534,29730193,38774343,
%U 84328391,317160458,371478595,600277187,811735945,849656112,139143919171
%N Engel expansion of real number x such that y = Gamma(x) is a minimum.
%C Gamma(x) has a minimum at x = 1.46163214496836234126265954232572132846819620400644... (A030169).
%H Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/constantsNumTheory.html">Some Constants from Number theory</a> from their "Numbers, constants and computation" web site.
%t 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 *)
%Y Cf. A030169.
%K nonn
%O 1,2
%A _Gerald McGarvey_, Jul 25 2004
%E Edited and extended by _Robert G. Wilson v_, Jul 28 2004
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