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%I #26 Sep 08 2022 08:46:00
%S 0,1,1,1,1,1,1,1,2,2,2,3,3,3,4,4,5,6,7,8,9,10,11,13,14,16,18,21,23,26,
%T 30,34,38,43,48,55,62,70,79,89,100,113,127,144,162,183,207,233,263,
%U 296,334,377,426,480,541,611,689,777,876,989,1115,1258,1418,1600,1804,2035,2295,2589,2920,3293,3714,4189,4725,5329,6010,6778
%N a(n) = floor(Fibonacci(n)^(1/4)).
%C The Ferraro problem asks for a proof that, for n>=9, floor(F(n)^(1/4)) = floor(F(n-4)^(1/4)+F(n-8)^(1/4)). As of November 2005 this problem remained unsolved.
%H Vincenzo Librandi, <a href="/A199575/b199575.txt">Table of n, a(n) for n = 0..1000</a>
%H P. J. Ferraro, <a href="http://www.fq.math.ca/Scanned/37-4/elementary37-4.pdf">Problem B-886</a>, Fibonacci Q., 37 (No. 4, Nov. 1999); 43 (No. 4, Nov. 2005), p. 372.
%H Raphael Schumacher, <a href="https://www.fq.math.ca/Problems/ElemProbSolnNov2020.pdf">Solution to Problem B-886</a>, Fibonacci Q., 58 (No. 4, Nov. 2020) pp. 368-370.
%t Table[Floor[Fibonacci[n]^(1/4)], {n, 0, 80}] (* _Vincenzo Librandi_, Aug 28 2016 *)
%o (Magma) [Floor(Fibonacci(n)^(1/4)): n in [0..80]]; // _Vincenzo Librandi_, Aug 28 2016
%o (PARI) a(n) = sqrtnint(fibonacci(n), 4); \\ _Michel Marcus_, Aug 28 2016
%Y Cf. A061287.
%K nonn
%O 0,9
%A _N. J. A. Sloane_, Nov 09 2011
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