A059187 Engel expansion of sqrt(Pi) = 1.77245... .

1, 2, 2, 12, 13, 90, 121, 3457, 7372, 42530, 147081, 348753, 1185480, 17262610, 28408922, 87175278, 120293961, 344697955, 634418862, 3889219736, 8965899278, 9695659687, 18962955420, 27004920068, 67070581522

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[Sqrt[Pi], 7!], 100] (* Modified by G. C. Greubel, Dec 27 2016 *)

Crossrefs

Cf. A002161 (sqrt(Pi)).

Sequence in context: A224497 A305753 A181813 * A350329 A265458 A054916

Adjacent sequences: A059184 A059185 A059186 * A059188 A059189 A059190

Keyword

nonn,easy,nice

Author

Mitch Harris

Status

approved