A059180 Engel expansion of log(2).

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

Offset: 1

Author

Mitch Harris

Keywords

• nonn
• easy
• nice

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]
• 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.
• Eric Weisstein's World of Mathematics, Engel Expansion
• Eric Weisstein's World of Mathematics, Natural Logarithm of 2
• 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

Crossrefs

Cf. A002162 (decimal expansion of the natural logarithm of 2).

Programs

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 *)