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A094683 Juggler sequence: if n mod 2 = 0 then floor(sqrt(n)) else floor(n^(3/2)).

%I A094683 #65 Feb 21 2025 22:12:19
%S A094683 0,1,1,5,2,11,2,18,2,27,3,36,3,46,3,58,4,70,4,82,4,96,4,110,4,125,5,
%T A094683 140,5,156,5,172,5,189,5,207,6,225,6,243,6,262,6,281,6,301,6,322,6,
%U A094683 343,7,364,7,385,7,407,7,430,7,453,7,476,7,500,8,524,8,548,8,573,8,598,8,623,8,649
%N A094683 Juggler sequence: if n mod 2 = 0 then floor(sqrt(n)) else floor(n^(3/2)).
%C A094683 Interspersion of A000093 and A000196. - _Michel Marcus_, Nov 11 2013
%D A094683 C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 233.
%H A094683 Karl V. Boddy, <a href="/A094683/b094683.txt">Table of n, a(n) for n = 0..10000</a>
%H A094683 Vikram Prasad and M. A. Prasad, <a href="https://doi.org/10.13140/RG.2.2.14110.04168">Estimates of the maximum excursion constant and stopping constant of juggler-like sequences</a>, ResearchGate, 2025.
%H A094683 Harry J. Smith, <a href="https://web.archive.org/web/20171111172551/http://www.reocities.com/hjsmithh/Juggler/JuggWhat.html">Juggler Sequence</a>
%H A094683 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JugglerSequence.html">Juggler Sequence</a>
%H A094683 Wikipedia, <a href="http://en.wikipedia.org/wiki/Juggler_sequence">Juggler sequence</a>
%p A094683 A094683 :=proc(n) if n mod 2 = 0 then RETURN(floor(sqrt(n))) else RETURN(floor(n^(3/2))); end if; end proc;
%t A094683 Table[If[EvenQ[n], Floor[Sqrt[n]], Floor[n^(3/2)]], {n, 0, 100}] (* _Indranil Ghosh_, Apr 07 2017 *)
%o A094683 (PARI) a(n) = if(n%2,sqrtint(n^3), sqrtint(n)); \\ _Indranil Ghosh_, Apr 08 2017
%o A094683 (Python)
%o A094683 import math
%o A094683 from sympy import sqrt
%o A094683 def a(n): return int(math.floor(sqrt(n))) if n%2 == 0 else int(math.floor(n**(3/2)))
%o A094683 print([a(n) for n in range(51)]) # _Indranil Ghosh_, Apr 08 2017
%o A094683 (Python)
%o A094683 from math import isqrt
%o A094683 def A094683(n): return isqrt(n**3 if n % 2 else n) # _Chai Wah Wu_, Feb 18 2022
%Y A094683 Cf. A007320, A007321, A094684, A094685, A094716.
%Y A094683 Cf. A000093, A000196.
%K A094683 nonn
%O A094683 0,4
%A A094683 _N. J. A. Sloane_, Jun 09 2004