A051392 First differences of A052006.

13, 13, 10, 13, 13, 10, 13, 13, 10, 13, 13, 10, 13, 13, 13, 10, 13, 13, 10, 13, 13, 10, 13, 13, 13, 10, 13, 13, 10, 13, 13, 10, 13, 13, 13, 10, 13, 13, 10, 13, 13, 10, 13, 13, 10, 13, 13, 13, 10, 13, 13, 10

Offset: 1

Author

Antti Karttunen and Patrick De Geest, Nov 15 1999

Keywords

• nonn
• nice

Comments

Does this sequence only contain 10's and 13's?

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1650

Programs

Mathematica

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 (* Jean-François Alcover, Feb 27 2016 *)