cp's OEIS Frontend

A060723 a(n) is the denominator of r(n) where r(n) is the sequence of rational numbers defined by the recursion: r(0) = 0, r(1) = 1 and for n>1 r(n) = r(n-1) + r(n-2)/2. From this definition it is clear that a(n) is always a power of 2 (see A060755).

%I A060723 #24 Mar 24 2020 08:40:37
%S A060723 1,1,1,2,1,4,4,8,1,16,16,32,8,64,64,128,8,256,256,512,128,1024,1024,
%T A060723 2048,256,4096,4096,8192,2048,16384,16384,32768,1024,65536,65536,
%U A060723 131072,32768,262144,262144,524288,65536,1048576,1048576,2097152
%N A060723 a(n) is the denominator of r(n) where r(n) is the sequence of rational numbers defined by the recursion: r(0) = 0, r(1) = 1 and for n>1 r(n) = r(n-1) + r(n-2)/2. From this definition it is clear that a(n) is always a power of 2 (see A060755).
%C A060723 It can be proved that r(n) is an integer (i.e. a(n) = 1) if and only if n is one of 0, 1, 2, 4, 8.
%F A060723 r(n) = (((1/2)*(sqrt(3) + 1))^n - ((1/2)*(sqrt(3) - 1))^n * cos(Pi*n))/sqrt(3). - _Peter Luschny_, Jun 02 2018
%e A060723 The sequence r(n) begins 0, 1, 1, 3/2, 2, 11/4, 15/4, 41/8, 7, 153/16, 209/16, 571/32, 363/16, 2023/64, 2749/64, 7521/128, 5135/64, ...
%t A060723 Denominator[RecurrenceTable[{a[0]==0,a[1]==1,a[n]==a[n-1]+a[n-2]/2},a,{n,50}]] (* _Harvey P. Dale_, Mar 07 2016 *)
%t A060723 Table[Denominator[Simplify[((1/2(1 + Sqrt[3]))^x - (1/2(Sqrt[3] - 1))^x Cos[Pi x])/ Sqrt[3]]], {x, 0, 43}]  (* _Peter Luschny_, Jun 02 2018 *)
%Y A060723 Cf. A060755, A305491 (numerators).
%K A060723 nonn,easy
%O A060723 0,4
%A A060723 Avi Peretz (njk(AT)netvision.net.il), Apr 21 2001
%E A060723 More terms from _Vladeta Jovovic_, Apr 24 2001