A278766 Engel expansion of plastic constant (real root of x^3 - x - 1).

1, 4, 4, 6, 6, 27, 74, 86, 372, 853, 947, 1475, 3686, 9084, 19174, 30737, 1530833, 2401466, 2521253, 3649563, 3802245, 9320024, 1092256819, 2114664794, 2878948610, 8842525055, 13769551820, 26996892389, 215947176106, 269439735691, 13694290818678, 18312336654245, 19649485782723, 63266709043539

Offset: 1

Author

Ilya Gutkovskiy, Nov 28 2016

Keywords

• nonn
• easy

Examples

			(1/2+sqrt(23/108))^(1/3) + (1/2-sqrt(23/108))^(1/3) = 1.324717957244... = 1/1 + 1/(1*4) + 1/(1*4*4) + 1/(1*4*4*6) + 1/(1*4*4*6*6) + 1/(1*4*4*6*6*27) + ...
		

Links

• Eric Weisstein's World of Mathematics, Engel Expansion
• Eric Weisstein's World of Mathematics, Plastic Constant
• Index entries for sequences related to Engel expansions

Crossrefs

Cf. A006784 (for definition of Engel expansion).

Cf. A060006, A072117.

Programs

Mathematica

EngelExp[A_, n_]:=Join[Array[1&, Floor[A]], First@Transpose@NestList[{Ceiling[1/Expand[ #[[1]]#[[2]]-1]], Expand[ #[[1]]#[[2]]-1]}&, {Ceiling[1/(A-Floor[A])], A-Floor[A]}, n-1]]; EngelExp[N[(1/2 + Sqrt[23/108])^(1/3) + (1/2 - Sqrt[23/108])^(1/3), 7! ], 40]