A380891 -id:A380891 - cp's OEIS frontend

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

James C. McMahon and Vikram Prasad, Apr 17 2025

nonn

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

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.

Cf. A380891, A383135.

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]

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))

A383135 a(n) = number of iterations that n requires to reach 1 under the x -> A380891(x) map, or -1 if it never does.

Original entry on oeis.org

0, 1, 2, 1, 3, 1, 5, 2, 3, 2, 3, 2, 4, 2, 4, 2, 6, 2, 4, 2, 6, 2, 13, 2, 13, 2, 8, 3, 8, 3, 10, 3, 10, 3, 3, 3, 10, 3, 5, 3, 10, 3, 5, 3, 5, 3, 6, 3, 5, 3, 5, 3, 17, 3, 5, 3, 5, 3, 17, 3, 3, 3, 3, 2, 12, 2, 3, 2, 5, 2, 5, 2, 12, 2, 3, 2, 7, 2, 3, 2, 7, 2, 7, 2

Offset: 1

James C. McMahon and Vikram Prasad, Apr 17 2025

nonn

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

The map x -> A380891(x) is conjectured to eventually reach 1 for all starting x > 0. Tested for x <= 7892481.

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.

Cf. A380891, A381246.

Cf. A006577.

fj[n_]:=If[Mod[n,2]==0,Floor[Surd[n,3]],Floor[n^(4/3)]];a383135[n_]:= Length[ NestWhileList[fj, n, # != 1 &]] - 1; Array[ a383135, 84]

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

cp's OEIS Frontend

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

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