A067920 Engel expansion of sin(2).

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

Offset: 1

Author

Benoit Cloitre, Mar 03 2002

Keywords

• easy
• nonn

Crossrefs

See A006784 for explanation of Engel expansions.

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

PARI

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

Extensions

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