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A261585 Number of sexagesimal digits of Fibonacci numbers in base-60 representation.

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%I A261585 #20 Jul 19 2025 19:00:39
%S A261585 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,
%T A261585 4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,
%U A261585 8,8,9,9,9,9,9,9,9,9,9,10,10,10,10,10
%N A261585 Number of sexagesimal digits of Fibonacci numbers in base-60 representation.
%C A261585 a(n) = length of n-th row in table A261575.
%C A261585 a(n)/n tends towards log_60(phi) = 0.117530856953191562796405213751... - _Hans J. H. Tuenter_, Jul 13 2025
%H A261585 Reinhard Zumkeller, <a href="/A261585/b261585.txt">Table of n, a(n) for n = 0..10000</a>
%H A261585 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sexagesimal.html">Sexagesimal</a>
%H A261585 Wikipedia, <a href="http://www.wikipedia.org/wiki/Sexagesimal">Sexagesimal</a>
%F A261585 For n>1, a(n) = 1+floor(n*log_60(phi)-log_60(5)/2), where phi=(1+sqrt(5))/2, the golden ratio. - _Hans J. H. Tuenter_, Jul 13 2025.
%t A261585 Join[{1}, IntegerLength[Fibonacci[Range[100]], 60]] (* _Paolo Xausa_, Feb 19 2024 *)
%o A261585 (Haskell)
%o A261585 a261585 = length . a261575_row
%Y A261585 Cf. A261575, A000045, A001622, A060384.
%K A261585 nonn,base
%O A261585 0,12
%A A261585 _Reinhard Zumkeller_, Sep 09 2015