A383135 Contribution to the OEIS (supporting a juggler sequence)

 

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

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

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OFFSET

1,3

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.

MATHEMATICA

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]

PROG

(Python)

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))

CROSSREFS

Cf. A380891, A381246.

Cf. A006577.

Sequence in context: A277120 A104725 A289079 * A249810 A257111 A011129

Adjacent sequences: A383132 A383133 A383134 * A383136 A383137 A383138

KEYWORD

nonn,new

AUTHOR

James C. McMahon and Vikram Prasad, Apr 17 2025

STATUS

approved