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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 30 20:58 EDT 2023. Contains 365796 sequences. (Running on oeis4.)