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%I #9 Nov 20 2020 20:41:29
%S 2,2,2,4,11,14,57,100,1778,2355,7690,21334,89831,126718,365351,665175,
%T 914152,1469797,3554254,25042522,190651419,580715831,1803513148,
%U 3705699670,44927205487,232354919706,1600668490436,7538452976365,12294187702836,28817421277388
%N Engel expansion of sin(2).
%t 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 *)
%o (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] */
%Y See A006784 for explanation of Engel expansions.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, Mar 03 2002
%E a(1)=2 inserted and a(29),a(30) from _Georg Fischer_, Nov 20 2020
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