A161368 Engel expansion of sqrt(7).

1, 1, 2, 4, 7, 7, 8, 14, 16, 21, 36, 40, 41, 354, 407, 568, 2253, 2392, 6783, 8608, 10968, 23813, 149663, 1353193, 2273258, 11992211, 18888350, 35589752, 279408946, 926928928, 7122445646, 12200380022, 24793374441, 1006675801235

Offset

1,3

Links

Table of n, a(n) for n=1..34.

Index to sequences related to Engel expansions

Example

2.645751311... = 1/1+1/(1*1)+1/(1*1*2)+1/(1*1*2*4)+1/(1*1*2*4*7)+1/(1*1*2*4*7*7)+....

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[7^(1/2), 7! ], 50]

Crossrefs

Cf. A010465, A059176.

Sequence in context: A161211 A276807 A363166 * A023978 A152488 A109359

Adjacent sequences: A161365 A161366 A161367 * A161369 A161370 A161371

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 08 2009

Extensions

Added example and link to index - R. J. Mathar, Sep 23 2009

Status

approved