cp's OEIS Frontend

A071996 a(1) = 0, a(2) = 1, a(n) = a(floor(n/3)) + a(n - floor(n/3)).

%I A071996 #17 Aug 22 2015 15:53:02
%S A071996 0,1,1,1,1,2,2,3,3,3,4,4,4,4,4,5,5,6,6,6,6,6,7,8,8,9,9,9,9,9,9,9,10,
%T A071996 11,12,12,12,13,13,13,13,13,13,13,13,13,13,14,15,16,16,17,17,18,18,19,
%U A071996 19,19,19,19,19,19,19,19,19,19,19,19,20,20,21,22,23,24,24,24,25,26,26,27
%N A071996 a(1) = 0, a(2) = 1, a(n) = a(floor(n/3)) + a(n - floor(n/3)).
%C A071996 "Rauzy's sequence" with initial values 0, 1.
%C A071996 David Moews showed that a(n)/n converges to about 0.31244. - _Jim Nastos_, Jan 08 2003
%C A071996 Difference of consecutive terms is always 0 or 1
%H A071996 Gheorghe Coserea, <a href="/A071996/b071996.txt">Table of n, a(n) for n = 1..10000</a>
%H A071996 David Moews, <a href="http://djm.cc/dmoews/rauzy.pdf">Asymptotic behavior of Rauzy's sequence</a>
%H A071996 Jeffrey Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/Talks/pmc2.ps">Ten Problems I Can't Solve (1.1MB ps)</a>
%t A071996 a[1]=0; a[2]=1; a[n_] := a[n]=a[Floor[n/3]]+a[n-Floor[n/3]]; Table[a[n], {n, 1, 75}]
%o A071996 (PARI)
%o A071996 n = 33; v = vector(n); v[1] = 'x; v[2] = 'y;
%o A071996 for(i = 3, n, v[i] = v[floor(i/3)] + v[i - floor(i/3)]);
%o A071996 apply(e -> polcoeff(e, 1, v[2]), v) \\ _Gheorghe Coserea_, Aug 22 2015
%Y A071996 Cf. A071991, A071995.
%K A071996 easy,nonn
%O A071996 1,6
%A A071996 _Jim Nastos_, Jun 17 2002
%E A071996 Edited by _Robert G. Wilson v_, Jun 23 2002