A059185 Engel expansion of Pi^2 = 9.8696...

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 9, 28, 45, 72, 111, 329, 415, 846, 1488, 5684, 1895742, 2890879, 5388452, 18083303, 30915293, 32699271, 38719784, 70637726, 118179186, 151342409, 995604288, 1839673662, 5342025157

Offset

1,10

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 and T. D. Noe, Table of n, a(n) for n = 1..1000 (terms 1 to 300 from T. D. Noe; terms 301 to 1000 from G. C. Greubel, Dec 27 2016)

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[Pi^2, 7!], 100] (* modified by G. C. Greubel, Dec 27 2016 *)

Crossrefs

Cf. A002388 (Pi^2).

Sequence in context: A302635 A302427 A303197 * A302309 A303040 A302877

Adjacent sequences: A059182 A059183 A059184 * A059186 A059187 A059188

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved