A242995 -id:A242995 - cp's OEIS frontend

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

Leroy Quet, Jan 30 2007

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

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

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

Cf. A127815, A242995.

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 *)

Extended by Ray Chandler, Feb 07 2007

A242996 a(n) = (a(n-1)^2 - a(n-2)^4) * a(n-1) / a(n-2)^2 with a(1) = 1, a(2) = 2.

Original entry on oeis.org

1, 2, 6, 30, -330, 257070, 128005692870, 23279147893155496537470, 388475314992168993748220639081347493631827670

Offset: 1

Michael Somos, Aug 17 2014

sign

The next term (a(10)) has 90 digits and a(11) has 178 digits. - Harvey P. Dale, Feb 23 2023

G. C. Greubel, Table of n, a(n) for n = 1..13

Cf. A127815, A242995.

I:=[1,2]; [n le 2 select I[n] else (Self(n-1)^2 - Self(n-2)^2 )/Self(n-2)^2: n in [1..10]]; // G. C. Greubel, Aug 06 2018

RecurrenceTable[{a[n] == (a[n-1]^2 - a[n-2]^4)*a[n-1]/a[n-2]^2, a[1] == 1, a[2] == 2}, a, {n, 1, 10}] (* G. C. Greubel, Aug 06 2018; corrected by Georg Fischer, Dec 07 2023 *)
nxt[{a_,b_}]:={b,(b^2-a^4) b/a^2}; NestList[nxt,{1,2},10][[;;,1]] (* Harvey P. Dale, Feb 23 2023 *)

{a(n) = if( n<3, max(0, n), my(x = a(n-2)^2, y = a(n-1)); (y^2 - x^2) * y / x)};

abs(a(n)) = A127815(n).
a(n+1) = a(n) * A242995(n) for all n>0.
0 = a(n)^2*a(n+2) + a(n+1)*(a(n)^4 - a(n+1)^2) for all n>0.

cp's OEIS Frontend

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

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