login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A059192
Engel expansion of log(1/gamma) (where gamma is the Euler-Mascheroni constant A001620) = 0.549539...
1
2, 11, 12, 13, 53, 348, 5263, 9960, 17040, 33193, 72960, 125350, 663179, 1096815, 3481893, 4802237, 7782503, 9659740, 279957736, 454935116, 460488754, 1710020367, 51367039980, 55286622194, 323648965384, 2061149370731
OFFSET
1,1
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
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.
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[1/EulerGamma], 7!], 100] (* Modified by G. C. Greubel, Dec 27 2016 *)
CROSSREFS
Cf. A002389.
Sequence in context: A137904 A175414 A359220 * A087339 A345922 A216213
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved