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A051392
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First differences of A052006.
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2
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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