A381246 -id:A381246 - cp's OEIS frontend

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

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])

cp's OEIS Frontend

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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