%I
%S 13,13,10,13,13,10,13,13,10,13,13,10,13,13,13,10,13,13,10,13,13,10,13,
%T 13,13,10,13,13,10,13,13,10,13,13,13,10,13,13,10,13,13,10,13,13,10,13,
%U 13,13,10,13,13,10
%N First differences of A052006.
%C Does this sequence only contain 10's and 13's?
%C Yes. Since all blocks of terms of A052005 are of the form 1(12)n, a(n) must be congruent to 1 modulo 3. [1, 2] blocks give an average growth rate of 3/2 powers of phi for every power of two, but since phi^3 > 4, singleton 1's are required to slow growth when errors get too large. Since singleton 1's reduce the growth rate by 1/2 power of phi per power of two, they should occur roughly once every (1/2) / log_2(phi^1.5 / 2) ~ 12.088 powers of phi. Therefore, a(n) will be 13 most of the time, with 10 occurring when needed to maintain this ratio.  _Charlie Neder_, Oct 24 2018
%H Vincenzo Librandi, <a href="/A051392/b051392.txt">Table of n, a(n) for n = 1..1650</a>
%t With[{F = Fibonacci}, Reap[For[n = 0, n < 1000, n++, If[F[n  1] < 2^Floor[Log[2, F[n]]] && F[n + 1] >= 2^(Floor[Log[2, F[n]]] + 1) && F[n + 2] >= 2^(Floor[Log[2, F[n]]] + 2), Sow[n]]]][[2, 1]]] // Differences (* _JeanFrançois Alcover_, Feb 27 2016 *)
%K nonn,nice
%O 1,1
%A _Antti Karttunen_ and _Patrick De Geest_, Nov 15 1999
