A059188 Engel expansion of Gamma(1/3) = 2.6789385....

1, 1, 2, 3, 14, 33, 57, 236, 6280, 7170, 172302, 24568434, 32871132, 43231756, 60680523, 83128444, 720494727, 803406064, 1804216488, 6655647717, 9106036988, 14962799365, 37839117297, 121819278396, 262108609568

Offset

1,3

Comments

Cf. A006784 for definition of Engel expansion.

References

F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.

Links

Table of n, a(n) for n=1..25.

F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.

P. Erdős and Jeffrey Shallit, New bounds on the length of finite Pierce and Engel series, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.

Index entries for sequences related to Engel expansions

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 ] ]

Crossrefs

Cf. A006784, A073005.

Sequence in context: A296149 A355176 A346606 * A080768 A370616 A203578

Adjacent sequences: A059185 A059186 A059187 * A059189 A059190 A059191

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved