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A059188 Engel expansion of Gamma(1/3) = 2.67894. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

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.

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.

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

Sequence in context: A080017 A042551 A296149 * A080768 A203578 A281486

Adjacent sequences:  A059185 A059186 A059187 * A059189 A059190 A059191

KEYWORD

nonn,easy,nice

AUTHOR

Mitch Harris

STATUS

approved

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Last modified January 22 12:13 EST 2019. Contains 319363 sequences. (Running on oeis4.)