A127815 -id:A127815 - 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.

A125676 a(n) = floor(abs(b(n))), where b(1) = 2, b(n) = b(n-1) - 1/b(n-1).

Original entry on oeis.org

2, 1, 0, 0, 2, 1, 1, 0, 0, 0, 0, 1, 1, 0, 3, 3, 3, 2, 2, 1, 1, 0, 1, 0, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 22, 22, 22, 22, 22, 22, 22, 22

Offset: 1

Leroy Quet, Jan 30 2007

nonn

Cf. A127814, A127815.

f[l_List] := Append[l, l[[ -1]] - 1/l[[ -1]]];Floor /@ Abs /@ Nest[f, {2}, 30] (* Ray Chandler, Feb 08 2007 *)

lista(nn) = my(b=2); print1(2); for(n=2, nn, print1(", ", floor(abs(b-=1/b)))); \\ Jinyuan Wang, Aug 10 2021

a(9)-a(31) from Ray Chandler, Feb 08 2007

More terms from Jinyuan Wang, Aug 10 2021

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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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.

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A125676 a(n) = floor(abs(b(n))), where b(1) = 2, b(n) = b(n-1) - 1/b(n-1).

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