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A067920 Engel expansion of sin(2). 0
2, 2, 2, 4, 11, 14, 57, 100, 1778, 2355, 7690, 21334, 89831, 126718, 365351, 665175, 914152, 1469797, 3554254, 25042522, 190651419, 580715831, 1803513148, 3705699670, 44927205487, 232354919706, 1600668490436, 7538452976365, 12294187702836, 28817421277388 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..30.

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[2], 7!], 30] (* Georg Fischer, Nov 20 2020 *)

PROG

(PARI): r=sin(2); for(i=1, 20, s=r*ceil(1/r)-1; print1(ceil(1/r), ", "); r=s); /* Benoit Cloitre [amended by Georg Fischer, Nov 20 2020] */

CROSSREFS

See A006784 for explanation of Engel expansions.

Sequence in context: A130707 A131562 A260786 * A107902 A142974 A259856

Adjacent sequences:  A067917 A067918 A067919 * A067921 A067922 A067923

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Mar 03 2002

EXTENSIONS

a(1)=2 inserted and a(29),a(30) from Georg Fischer, Nov 20 2020

STATUS

approved

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Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)