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
Keywords
Examples
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)+....
Programs
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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]
Extensions
Added example and link to index - R. J. Mathar, Sep 23 2009