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 A059180 Engel expansion of log(2). 3
 2, 3, 7, 9, 104, 510, 1413, 2386, 40447, 87110, 124975, 1565154, 1766158, 2440919, 2637001, 9192874, 24998746, 73973182, 88828340, 432049320, 470421590, 477600793, 3313014448, 4571423959, 28839435286, 40818751774 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A006784 for the 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] Eric Weisstein's World of Mathematics, Engel Expansion Eric Weisstein's World of Mathematics, Natural Logarithm of 2 P. ErdÅ‘s 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[Log[2], 7!], 100] (* Modified by G. C. Greubel, Dec 27 2016 *) CROSSREFS Cf. A002162 (decimal expansion of the natural logarithm of 2). Sequence in context: A107861 A109800 A152136 * A051637 A051471 A140794 Adjacent sequences:  A059177 A059178 A059179 * A059181 A059182 A059183 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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