A067921 Engel expansion of sqrt(Pi/2).

1, 4, 76, 134, 213, 1649, 1955, 2041, 32363, 217167, 760577, 1633080, 6412486, 24932290, 25544312, 376841489, 426956719, 472747939, 765965856, 2708004694, 5814287795, 14630348817, 21857959576, 92077240148, 184486528542

Offset: 1

Author

Benoit Cloitre, Mar 03 2002

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

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[Sqrt[Pi/2], 7!], 50] (* G. C. Greubel, Jan 12 2017 *)

PARI

s=sqrt(asin(1)); for(i=1,30,s=s*ceil(1/s)-1; print1(ceil(1/s),","); );