A059181 Engel expansion of log(3) = 1.09861... .

1, 11, 12, 60, 108, 139, 176, 1228, 1356, 3166, 14807, 81596, 116387, 1367315, 4408018, 11560054, 15330821, 448349063, 574897948, 613663772, 636869505, 999446566, 3786082000, 6911150147, 19780703830, 25945009665, 33227233233, 103529753474, 118556676397

Offset

1,2

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

G. C. Greubel, Table of n, a(n) for n = 1..1000

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]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]];
EngelExp[N[Log[3], 7!], 100] (* Modified by G. C. Greubel, Dec 27 2016 *)

Crossrefs

Cf. A002391.

Sequence in context: A291059 A041254 A041256 * A041258 A082262 A239463

Adjacent sequences: A059178 A059179 A059180 * A059182 A059183 A059184

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved