A067919 Engel expansion of sin(1).
2, 2, 3, 11, 14, 27, 28, 66, 212, 231, 552, 2842, 3774, 6038, 6784, 10950, 32948, 78591, 97875, 98342, 123569, 139837, 159698, 1102838, 3256476, 20329622, 34385124, 60999878, 82669919, 85820365, 389915995, 4274338879, 18907353107, 62875944378, 74931184173
Offset: 1
Examples
sin(1) = 0.84147... = A049469 has the Engel expansion 1/2 + 1/(2*2) + 1/(2*2*3) + ...
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[Sin[1],6! ],50] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2009 *) -
PARI
s=sin(1); for(i=1,30,s=s*ceil(1/s)-1; print1(ceil(1/s),","); );
Extensions
a(1) inserted by Hauke Worpel (hw1(AT)email.com), Jun 01 2003
Edited by N. J. A. Sloane, Nov 01 2008 at the suggestion of R. J. Mathar