A096188 Engel expansion of real number x such that y = Gamma(x) is a minimum.

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

Offset: 1

Author

Gerald McGarvey, Jul 25 2004

Keywords

• nonn

Comments

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

Links

• Xavier Gourdon and Pascal Sebah, Some Constants from Number theory from their "Numbers, constants and computation" web site.

Crossrefs

Cf. A030169.

Programs

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 *)

Extensions

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