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

1, 2, 4, 4, 8, 6, 30, 8, 18, 10, 24, 12, 30, 14, 36, 16, 150, 18, 50, 20, 1320, 22, 43366048, 24, 41678, 26, 350, 28, 41678, 30, 234421146, 32, 2438232, 34, 114, 36, 5184, 38, 132, 40, 124026, 42, 150, 44, 160, 46, 934, 48, 1008, 50, 1084, 52, 43366048, 54, 1240

Offset: 1

Author

James C. McMahon and Vikram Prasad, Apr 17 2025

Keywords

• nonn

Comments

A380891(x) map is If x mod 2 = 0 then a(x) = floor(x^(1/3)) else a(x) = floor(x^(4/3)).

Links

• James C. McMahon, Table of n, a(n) for n = 1..10000
• Vikram Prasad and M. A. Prasad, Estimates of the maximum excursion constant and stopping constant of juggler-like sequences, ResearchGate, 2025.

Crossrefs

Cf. A380891, A383135.

Programs

Mathematica

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]

Python

import sys
import gmpy2
sys.set_int_max_str_digits(0)
def floorJuggler(n):
    a=n
    max=n
    while a > 1:
        b=0
        if a%2 == 0:
            b1=gmpy2.iroot(a,3)
            b=b1[0]
        else:
            b1=gmpy2.iroot(a**4,3)
            b=b1[0]
        a=b
        if a > max:
            max = a
    return max
maxcount=0
for i in range (1, 100):
    print (i, floorJuggler(i))