A059190 - OEIS

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A059190

Engel expansion of gamma^2, (gamma is the Euler-Mascheroni constant A001620) = 0.333178.

4, 4, 4, 4, 4, 6, 23, 26, 126, 132, 154, 269, 421, 911, 1899, 7335, 14245, 34244, 78354, 173699, 239896, 247397, 659900, 1646344, 2454988, 6831657, 65833355, 839918922, 1187969748, 3583279448, 4114383765, 6590212761, 11304687651

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OFFSET

1,1

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

CROSSREFS

Cf. A155969.

Sequence in context: A091844 A244157 A103276 * A085142 A064053 A108893

Adjacent sequences: A059187 A059188 A059189 * A059191 A059192 A059193

KEYWORD

nonn,easy,nice

AUTHOR

Mitch Harris

STATUS

approved