A066356 Numerator of sequence defined by recursion c(n) = 1 + c(n-2) / c(n-1), c(0) = 0, c(1) = 1.

0, 1, 1, 2, 3, 7, 23, 167, 3925, 661271, 2609039723, 1728952269242533, 4516579101127820242349159, 7812958861560974806259705508894834509747, 35298563436210937269618773778802420542715366288238091341051372773

Offset

0,4

Comments

a(i) and a(j) are relative prime for all i>j>0.

An infinite coprime sequence defined by recursion.

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = (2 * a(n - 1) * a(n - 2)^2 - a(n - 1)^2 * a(n - 4) - a(n - 2)^3 * a(n - 3)) / (a(n - 2) - a(n - 3) * a(n - 4)).

a(n) = b(n) + b(n-1) * a(n-2) where b(n) = A064184(n).

Mathematica

nxt[{a_, b_}]:={b, 1+a/b}; NestList[nxt, {0, 1}, 20][[All, 1]]//Numerator (* Harvey P. Dale, Sep 26 2016 *)

Prog

(PARI) {a(n) = if( n<4, max(0, n) - (n>1), (2 * a(n-1) * a(n-2)^2 - a(n-1)^2 * a(n-4) - a(n-2)^3 * a(n-3)) / (a(n-2) - a(n-3) * a(n-4)))}

Crossrefs

Cf. A001685, A002715, A003686, A006695, A064184 (denominators), A064526.

Sequence in context: A001064 A108176 A111235 * A006892 A296397 A102710

Adjacent sequences: A066353 A066354 A066355 * A066357 A066358 A066359

Keyword

nonn,easy

Author

Michael Somos, Dec 21 2001

Status

approved