A381246 Contribution to the OEIS (supporting a juggler sequence)

 A381246

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

0

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

(list; graph; refs; listen; history; edit; text; internal format)

OFFSET

1,2

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)]]; a381246[n_]:=Max[Delete[FixedPointList[fj, n], -1]]; Array[a381246, 55]

PROG

(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))

CROSSREFS

Cf. A380891, A383135.

Sequence in context: A117295 A235999 A093820 * A095400 A237264 A265560

Adjacent sequences: A381243 A381244 A381245 * A381247 A381248 A381249

KEYWORD

nonn,new

AUTHOR

James C. McMahon and Vikram Prasad, Apr 17 2025

STATUS

approved