|
|
A059187
|
|
Engel expansion of sqrt(Pi) = 1.77245... .
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
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.
|
|
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
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|