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A381246 Largest value in trajectory of n under the juggler map of A380891.

%I A381246 #23 Apr 30 2025 23:27:57
%S A381246 1,2,4,4,8,6,30,8,18,10,24,12,30,14,36,16,150,18,50,20,1320,22,
%T A381246 43366048,24,41678,26,350,28,41678,30,234421146,32,2438232,34,114,36,
%U A381246 5184,38,132,40,124026,42,150,44,160,46,934,48,1008,50,1084,52,43366048,54,1240
%N A381246 Largest value in trajectory of n under the juggler map of A380891.
%C A381246 A380891(x) map is If x mod 2 = 0 then a(x) = floor(x^(1/3)) else a(x) = floor(x^(4/3)).
%H A381246 James C. McMahon, <a href="/A381246/b381246.txt">Table of n, a(n) for n = 1..10000</a>
%H A381246 Vikram Prasad and M. A. Prasad, <a href="https://www.researchgate.net/publication/387868199_ESTIMATES_OF_THE_MAXIMUM_EXCURSION_CONSTANT_AND_STOPPING_CONSTANT_OF_JUGGLER-LIKE_SEQUENCES">Estimates of the maximum excursion constant and stopping constant of juggler-like sequences</a>, ResearchGate, 2025.
%t A381246 fj[n_]:=If[Mod[n,2]==0,Floor[Surd[n,3]],Floor[n^(4/3)]];a381246[n_]:=Max[Delete[FixedPointList[fj, n], -1]];Array[a381246,55]
%o A381246 (Python)
%o A381246 import sys
%o A381246 import gmpy2
%o A381246 sys.set_int_max_str_digits(0)
%o A381246 def floorJuggler(n):
%o A381246     a=n
%o A381246     max=n
%o A381246     while a > 1:
%o A381246         b=0
%o A381246         if a%2 == 0:
%o A381246             b1=gmpy2.iroot(a,3)
%o A381246             b=b1[0]
%o A381246         else:
%o A381246             b1=gmpy2.iroot(a**4,3)
%o A381246             b=b1[0]
%o A381246         a=b
%o A381246         if a > max:
%o A381246             max = a
%o A381246     return max
%o A381246 maxcount=0
%o A381246 for i in range (1, 100):
%o A381246     print (i, floorJuggler(i))
%Y A381246 Cf. A380891, A383135.
%K A381246 nonn
%O A381246 1,2
%A A381246 _James C. McMahon_ and _Vikram Prasad_, Apr 17 2025