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

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, 140, 5, 156, 5, 173, 6, 190, 6, 207, 6, 225, 6, 244, 6, 263, 6, 282, 7, 302, 7, 322, 7, 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

Offset: 0

Author

N. J. A. Sloane, Jun 09 2004

Keywords

• nonn

References

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000
• Vikram Prasad and M. A. Prasad, Estimates of the maximum excursion constant and stopping constant of juggler-like sequences, ResearchGate, 2025.
• Harry J. Smith, Juggler Sequence

Crossrefs

Cf. A007320, A007321, A094684, A094683, A094693, A094725.

Programs

Maple

f:=proc(n) if n mod 2 = 0 then RETURN(round(sqrt(n))) else RETURN(round(n^(3/2))); fi; end;

Mathematica

A094685[n_]:=If[Mod[n,2]==0,Round[Sqrt[n]],Round[n^(3/2)]];Array[A094685,76,0] (* James C. McMahon, Apr 15 2025 *)

Python

from gmpy2 import isqrt_rem
def A094685(n):
    i, j = isqrt_rem(n**3 if n % 2 else n)
    return int(i+ int(4*(j-i) >= 1)) # Chai Wah Wu, Aug 17 2016