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A094685 Modified juggler sequence: if n mod 2 = 0 then round(sqrt(n)) else round(n^(3/2)).

%I A094685 #22 Apr 15 2025 10:29:08
%S A094685 0,1,1,5,2,11,2,19,3,27,3,36,3,47,4,58,4,70,4,83,4,96,5,110,5,125,5,
%T A094685 140,5,156,5,173,6,190,6,207,6,225,6,244,6,263,6,282,7,302,7,322,7,
%U A094685 343,7,364,7,386,7,408,7,430,8,453,8,476,8,500,8,524,8,548,8,573,8,598,8,624,9,650
%N A094685 Modified juggler sequence: if n mod 2 = 0 then round(sqrt(n)) else round(n^(3/2)).
%D A094685 C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 233.
%H A094685 Chai Wah Wu, <a href="/A094685/b094685.txt">Table of n, a(n) for n = 0..10000</a>
%H A094685 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 A094685 Harry J. Smith, <a href="https://web.archive.org/web/20171111172551/http://www.reocities.com/hjsmithh/Juggler/JuggWhat.html">Juggler Sequence</a>
%p A094685 f:=proc(n) if n mod 2 = 0 then RETURN(round(sqrt(n))) else RETURN(round(n^(3/2))); fi; end;
%t A094685 A094685[n_]:=If[Mod[n,2]==0,Round[Sqrt[n]],Round[n^(3/2)]];Array[A094685,76,0] (* _James C. McMahon_, Apr 15 2025 *)
%o A094685 (Python)
%o A094685 from gmpy2 import isqrt_rem
%o A094685 def A094685(n):
%o A094685     i, j = isqrt_rem(n**3 if n % 2 else n)
%o A094685     return int(i+ int(4*(j-i) >= 1)) # _Chai Wah Wu_, Aug 17 2016
%Y A094685 Cf. A007320, A007321, A094684, A094683, A094693, A094725.
%K A094685 nonn
%O A094685 0,4
%A A094685 _N. J. A. Sloane_, Jun 09 2004