Vikram Prasad - 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))

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

Original entry on oeis.org

0, 1, 1, 4, 1, 8, 1, 13, 2, 18, 2, 24, 2, 30, 2, 36, 2, 43, 2, 50, 2, 57, 2, 65, 2, 73, 2, 81, 3, 89, 3, 97, 3, 105, 3, 114, 3, 123, 3, 132, 3, 141, 3, 150, 3, 160, 3, 169, 3, 179, 3, 189, 3, 199, 3, 209, 3, 219, 3, 229, 3, 240, 3, 250, 4, 261, 4, 272

Offset: 0

Vikram Prasad, Feb 08 2025

Interspersion of A048766 and A129011.

Cf. A094683, A381246, A383135.

a[n_]:=If[Mod[n,2]==0,Floor[n^(1/3)],Floor[n^(4/3)]]; (* James C. McMahon, Apr 11 2025 *)

import gmpy2
def a(n): return int(gmpy2.iroot(n**4 if n&1 else n, 3)[0])

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User: Vikram Prasad

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

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

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Python

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

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python