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

1,1

Links

Table of n, a(n) for n=1..35.

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.

Cf. A049469, A084651, A084652.

Sequence in context: A067579 A019143 A084650 * A157301 A143931 A143933

Adjacent sequences: A067916 A067917 A067918 * A067920 A067921 A067922

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