cp's OEIS Frontend

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

%I A066356 #10 Sep 22 2019 08:02:51
%S A066356 0,1,1,2,3,7,23,167,3925,661271,2609039723,1728952269242533,
%T A066356 4516579101127820242349159,7812958861560974806259705508894834509747,
%U A066356 35298563436210937269618773778802420542715366288238091341051372773
%N A066356 Numerator of sequence defined by recursion c(n) = 1 + c(n-2) / c(n-1), c(0) = 0, c(1) = 1.
%C A066356 a(i) and a(j) are relative prime for all i>j>0.
%C A066356 An infinite coprime sequence defined by recursion.
%F A066356 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)).
%F A066356 a(n) = b(n) + b(n-1) * a(n-2) where b(n) = A064184(n).
%t A066356 nxt[{a_,b_}]:={b,1+a/b}; NestList[nxt,{0,1},20][[All,1]]//Numerator (* _Harvey P. Dale_, Sep 26 2016 *)
%o A066356 (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)))}
%Y A066356 Cf. A001685, A002715, A003686, A006695, A064184 (denominators), A064526.
%K A066356 nonn,easy
%O A066356 0,4
%A A066356 _Michael Somos_, Dec 21 2001