A280092 Pierce Expansion of tan(1).

1, 1, 2, 8, 12, 44, 51, 298, 934, 1041, 2267, 2668, 13150, 28929, 42652, 610672, 1630027, 2535276, 5451792, 14793658, 32179208, 38644893, 45925185, 59151658, 80924233, 118811249, 273877246, 611892649, 1688111599, 11265859421, 22104337881, 31986803107, 104253472513

Offset: 0

Author

G. C. Greubel, Dec 25 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Pierce Expansion
• Wikipedia, Engel Expansion

Crossrefs

Cf. A049471 (tan(1)).

Programs

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[Tan[1] , 7!], 50]