A163168 Pierce expansion of sech(1).

1, 2, 3, 8, 9, 24, 37, 85, 1115, 29153, 423233, 2208087, 5102497, 9813637, 15922076, 19204759, 106559540, 120015709, 1493877142, 2199074984, 32818755269, 1505298832166, 1507229768977, 2841536357911, 14805574584765

Offset

1,2

Comments

Pierce expansion of A073746.

Links

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

Eric Weisstein, Pierce Expansion, Mathworld.

Formula

0.648054... = 1/1 - 1/(1*2) + 1/(1*2*3) - 1/(1*2*3*8) + 1/(1*2*3*8*9) - ...

Mathematica

PierceExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@ NestList[{Floor[1/Expand[1 - #[[1]] #[[2]]]], Expand[1 - #[[1]] #[[2]]]} &, {Floor[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; PierceExp[N[Sech[1] , 7!], 50] (* G. C. Greubel, Nov 14 2016 *)

Crossrefs

Sequence in context: A103026 A098506 A279090 * A085453 A271394 A030439

Adjacent sequences: A163165 A163166 A163167 * A163169 A163170 A163171

Keyword

nonn

Author

R. J. Mathar, Jul 22 2009

Status

approved