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

Author

Benoit Cloitre, Mar 03 2002

Keywords

• easy
• nonn

Examples

			sin(1) = 0.84147... = A049469 has the Engel expansion 1/2 + 1/(2*2) + 1/(2*2*3) + ...
		

Crossrefs

See A006784 for explanation of Engel expansions.

Cf. A049469, A084651, A084652.

Programs

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