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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.

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^2/6, 7!], 100] (* Modified by G. C. Greubel, Dec 27 2016 *)

CROSSREFS

Cf. A013661, A053980, A067912.

Sequence in context: A153776 A005625 A067785 * A034702 A167206 A053223

Adjacent sequences:  A059183 A059184 A059185 * A059187 A059188 A059189

KEYWORD

nonn,easy,nice

AUTHOR

Mitch Harris

STATUS

approved

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Last modified January 22 17:33 EST 2019. Contains 319365 sequences. (Running on oeis4.)