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Juggler sequence: if n mod 2 = 0 then floor(sqrt(n)) else floor(n^(3/2)).
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%I #55 Oct 03 2024 02:38:17

%S 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 140,5,156,5,172,5,189,5,207,6,225,6,243,6,262,6,281,6,301,6,322,6,

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

%C Interspersion of A000093 and A000196. - _Michel Marcus_, Nov 11 2013

%D C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 233.

%H Karl V. Boddy, <a href="/A094683/b094683.txt">Table of n, a(n) for n = 0..10000</a>

%H H. J. Smith, <a href="https://web.archive.org/web/20171111172551/http://www.reocities.com/hjsmithh/Juggler/JuggWhat.html">Juggler Sequence</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JugglerSequence.html">Juggler Sequence</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Juggler_sequence">Juggler sequence</a>

%p A094683 :=proc(n) if n mod 2 = 0 then RETURN(floor(sqrt(n))) else RETURN(floor(n^(3/2))); end if; end proc;

%t Table[If[EvenQ[n], Floor[Sqrt[n]], Floor[n^(3/2)]], {n, 0, 100}] (* _Indranil Ghosh_, Apr 07 2017 *)

%o (PARI) for(n=0, 100, print1(if(n%2, sqrtint(n^3), sqrtint(n)), ", ")) \\ _Indranil Ghosh_, Apr 08 2017

%o (Python)

%o import math

%o from sympy import sqrt

%o def a(n): return int(math.floor(sqrt(n))) if n%2 == 0 else int(math.floor(n**(3/2)))

%o print([a(n) for n in range(51)]) # _Indranil Ghosh_, Apr 08 2017

%o (Python)

%o from math import isqrt

%o def A094683(n): return isqrt(n**3 if n % 2 else n) # _Chai Wah Wu_, Feb 18 2022

%Y Cf. A007320, A007321, A094684, A094685, A094716.

%Y Cf. A000093, A000196.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Jun 09 2004