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A067919
Engel expansion of sin(1).
3
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
1,1
EXAMPLE
sin(1) = 0.84147... = A049469 has the Engel expansion 1/2 + 1/(2*2) + 1/(2*2*3) + ...
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 *)
PROG
(PARI) : s=sin(1); for(i=1, 30, s=s*ceil(1/s)-1; print1(ceil(1/s), ", "); );
CROSSREFS
See A006784 for explanation of Engel expansions.
Sequence in context: A067579 A019143 A084650 * A157301 A143931 A143933
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Mar 03 2002
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
STATUS
approved