A280094 Pierce Expansion of cot(1).

1, 2, 3, 6, 8, 12, 13, 15, 17, 19, 1063, 1155, 2574, 2662, 3595, 3723, 4370, 21530, 28927, 32662, 73255, 92895, 5133189, 13626701, 17852908, 392678721, 715595109, 3993107840, 39941257169, 43578446054, 1686996293054, 4244526044926, 78467829696572, 111290944386765

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. A073449 (cot(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[Cot[1] , 7!], 50]