cp's OEIS Frontend

A110091 Denominators of sequence of rationals defined by r(n) = n for n<=1 and for n>1: r(n) = (sum of denominators of r(n-1) and r(n-2))/(sum of numerators of r(n-1) and r(n-2)).

%I A110091 #10 Jun 17 2021 09:12:34
%S A110091 1,1,1,3,1,3,5,1,5,7,1,7,9,1,9,11,1,11,13,1,13,15,1,15,17,1,17,19,1,
%T A110091 19,21,1,21,23,1,23,25,1,25,27,1,27,29,1,29,31,1,31,33,1,33,35,1,35,
%U A110091 37,1,37,39,1,39,41,1,41,43,1,43,45,1,45,47,1,47,49,1,49,51,1,51,53,1,53,55
%N A110091 Denominators of sequence of rationals defined by r(n) = n for n<=1 and for n>1: r(n) = (sum of denominators of r(n-1) and r(n-2))/(sum of numerators of r(n-1) and r(n-2)).
%H A110091 G. C. Greubel, <a href="/A110091/b110091.txt">Table of n, a(n) for n = 0..1000</a>
%F A110091 a(3*k) = 2*k+1, a(3*k+1) = 1, a(3*k+2) = 2*k+1.
%F A110091 r(n) = A110090(n) / a(n).
%F A110091 a(n) = (A110090(n-1) + A110090(n-2))/GCD(a(n-1) + a(n-2), A110090(n-1) + A110090(n-2)).
%t A110091 a[n_]:= a[n]= If[Mod[n, 3]==0, 2*Floor[n/3] +1, If[Mod[n, 3]==1, 1, 2*Floor[n/3] +1]]; Table[a[n], {n, 0, 100}] (* _G. C. Greubel_, Jun 16 2021 *)
%o A110091 (Sage)
%o A110091 def A110091(n):
%o A110091     if (n%3==0): return 2*(n//3) + 1
%o A110091     elif (n%3==1): return 1
%o A110091     else: return 2*(n//3) +1
%o A110091 [A110091(n) for n in (0..100)] # _G. C. Greubel_, Jun 16 2021
%Y A110091 Cf. A110090 (numerators).
%K A110091 nonn,frac
%O A110091 0,4
%A A110091 _Reinhard Zumkeller_, Jul 14 2005