A127814 a(n) = numerator of b(n), where b(1) = 2, b(n) = b(n-1) - 1/b(n-1).

2, 3, 5, -11, 779, 497941, 181860254581, 16687694789137362648661, -263439569256003706800705587722279993788907979, 81512663708476146329709015825571064954724426915346799560162522434680208602364731247764459

Offset

1,1

Comments

Every term of this sequence of numerators is coprime to every other term.

Links

Table of n, a(n) for n=1..10.

M. Chamberland and M. Martelli, Unbounded Orbits and Binary Digits, Grinnell College.

Clark Kimberling, Polynomials associated with reciprocation, JIS 12 (2009) 09.3.4

Example

A127814/A127815 = 2, 3/2, 5/6, -11/30, 779/330, 497941/257070, 181860254581/128005692870, ...

Mathematica

f[l_List] := Append[l, l[[ -1]] - 1/l[[ -1]]]; Numerator[Nest[f, {2}, 10]] (* Ray Chandler, Feb 07 2007 *)
Numerator/@NestList[#-1/#&, 2, 10]  (* Harvey P. Dale, Apr 30 2011 *)

Crossrefs

Cf. A127815, A242995.

Sequence in context: A327428 A220346 A242995 * A162253 A321855 A357433

Adjacent sequences: A127811 A127812 A127813 * A127815 A127816 A127817

Keyword

easy,frac,sign

Author

Leroy Quet, Jan 30 2007

Extensions

Extended by Ray Chandler, Feb 07 2007

Status

approved