|
%I #13 Jul 03 2014 02:05:06
%S 1,1,2,3,3,4,5,5,6,7,7,8,8,9,10,11,12,12,12,13,13,14,15,16,16,17,18,
%T 19,20,20,20,20,21,21,22,23,24,25,26,27,27,28,28,28,29,30,31,32,33,33,
%U 33,33,33,34,34,35,36,37,38,38,39,40,41,42,43,44,45,46,46,47,47,47,48,48
%N a(1)=a(2)=1; for n >=3, a(n) = a(a(a(n-1))) + a(n-a(a(n-1))).
%C For n>1: a(n)<n*(phi-1) iff n is in A001519 where phi is the golden ratio = (1+sqrt(5))/2 - _Benoit Cloitre_, May 27 2004
%H J. Grytczuk, <a href="http://dx.doi.org/10.1016/j.disc.2003.10.022">Another variation on Conway's recursive sequence</a>, Discr. Math. 282 (2004), 149-161.
%H Abraham Isgur, Mustazee Rahman, <a href="http://arxiv.org/abs/1407.0425">On variants of Conway and Conolly's Meta-Fibonacci recursions</a>, arXiv:1407.0425 [math.CO], 2014.
%F a(A001519(n)) = floor((phi-1)*A001519(n)); a(A000045(n)) = A000045(n-1); liminf a(n)/n = phi-1; limsup a(n)/n = ? - _Benoit Cloitre_, May 27 2004
%t a[1] = a[2] = 1; a[n_] := a[n] = a[a[a[n - 1]]] + a[n - a[a[n - 1]]]; Table[ a[n], {n, 75}] (* _Robert G. Wilson v_, May 27 2004 *)
%o (PARI) {m=75;v=vector(m,j,1);for(n=3,m,a=v[v[v[n-1]]]+v[n-v[v[n-1]]];v[n]=a);for(j=1,m,print1(v[j],","))} \\ _Klaus Brockhaus_, May 27 2004
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, May 27 2004
%E More terms from _Benoit Cloitre_, _Robert G. Wilson v_ and _Klaus Brockhaus_, May 27 2004
|
