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%I #9 Jan 12 2017 14:56:37
%S 1,4,76,134,213,1649,1955,2041,32363,217167,760577,1633080,6412486,
%T 24932290,25544312,376841489,426956719,472747939,765965856,2708004694,
%U 5814287795,14630348817,21857959576,92077240148,184486528542
%N Engel expansion of sqrt(Pi/2).
%H G. C. Greubel, <a href="/A067921/b067921.txt">Table of n, a(n) for n = 1..1000</a>
%t EngelExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@
%t NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]} &, {Ceiling[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; EngelExp[N[Sqrt[Pi/2], 7!], 50] (* _G. C. Greubel_, Jan 12 2017 *)
%o (PARI) : s=sqrt(asin(1)); for(i=1,30,s=s*ceil(1/s)-1; print1(ceil(1/s),","); );
%Y See A006784 for explanation of Engel expansions.
%K easy,nonn
%O 1,2
%A _Benoit Cloitre_, Mar 03 2002