A108905 Engel series expansion for Sierpinski's constant.

1, 1, 2, 6, 51, 114, 136, 149, 1388, 3654, 3961, 41614, 2975365, 4120126, 5760908, 11210809, 21235067, 43239302, 156258546, 230627452, 595763433, 4709180601, 148918280487, 841708059551, 2895551449652, 5660433533409, 6575950336213

Offset: 0

Author

Hauke Worpel (hw1(AT)email.com), Jul 17 2005

Keywords

• nonn

Crossrefs

Cf. A062089, A006784.

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[ Pi(-Log[Pi] + 2EulerGamma + 4LogGamma[3/4]), 2^8], 25] (* Robert G. Wilson v *)

Extensions

a(11) - a(26) from Robert G. Wilson v, Jul 21 2005