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

Author

Leroy Quet, Jan 30 2007

Keywords

• easy
• frac
• sign

Comments

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

Examples

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

Links

• M. Chamberland and M. Martelli, Unbounded Orbits and Binary Digits, Grinnell College.
• Clark Kimberling, Polynomials associated with reciprocation, JIS 12 (2009) 09.3.4

Crossrefs

Cf. A127815, A242995.

Programs

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 *)

Extensions

Extended by Ray Chandler, Feb 07 2007