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%I #5 Mar 31 2012 12:38:24
%S 1,1,2,4,7,7,8,14,16,21,36,40,41,354,407,568,2253,2392,6783,8608,
%T 10968,23813,149663,1353193,2273258,11992211,18888350,35589752,
%U 279408946,926928928,7122445646,12200380022,24793374441,1006675801235
%N Engel expansion of sqrt(7).
%H <a href="/index/El#Engel">Index to sequences related to Engel expansions</a>
%e 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)+....
%t 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]
%Y Cf. A010465, A059176.
%K nonn
%O 1,3
%A _Vladimir Joseph Stephan Orlovsky_, Jun 08 2009
%E Added example and link to index - _R. J. Mathar_, Sep 23 2009
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