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A059186 Engel expansion of Pi^2/6, or zeta(2) = 1.64493. 3
1, 2, 4, 7, 9, 22, 35, 79, 2992, 3597, 17523, 28632, 41470, 53093, 57406, 14504930, 42622213, 188335162, 322429556, 1023003875, 1328535963, 3138645732, 11618168524, 137721814936, 156929353744, 166732460513, 813398686532 (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
G. C. Greubel and T. D. Noe, Table of n, a(n) for n = 1..1000[Terms 1 to 300 computed by T. D. Noe; Terms 301 to 1000 computed by 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.
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^2/6, 7!], 100] (* Modified by G. C. Greubel, Dec 27 2016 *)
CROSSREFS
Sequence in context: A005625 A340989 A067785 * A034702 A325745 A167206
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)