A389383 Triangle T(n,k): the n-th row gives the trajectory of n under the juggler map x->A094683(x) ending on 1.

1, 2, 1, 3, 5, 11, 36, 6, 2, 1, 4, 2, 1, 5, 11, 36, 6, 2, 1, 6, 2, 1, 7, 18, 4, 2, 1, 8, 2, 1, 9, 27, 140, 11, 36, 6, 2, 1, 10, 3, 5, 11, 36, 6, 2, 1, 11, 36, 6, 2, 1, 12, 3, 5, 11, 36, 6, 2, 1, 13, 46, 6, 2, 1, 14, 3, 5, 11, 36, 6, 2, 1, 15, 58, 7, 18, 4, 2, 1, 16, 4, 2, 1

Offset

1,2

Links

Saeed Hatami Boura, Table of n, a(n) for n = 1..10631

Wikipedia, Juggler sequence.

Example

Irregular table T(n,k) begins:
  n\k    0     1     2     3     4     5    6   7   8   9   10  11
  -----------------------------------------------------------------
   1:    1
   2:    2     1
   3:    3     5    11    36     6     2    1
   4:    4     2     1
   5:    5    11    36     6     2     1
   6:    6     2     1
   7:    7    18     4     2     1
   8:    8     2     1
   9:    9    27   140    11    36     6    2   1
  10:   10     3     5    11    36     6    2   1
  11:   11    36     6     2     1
  12:   12     3     5    11    36     6    2   1
  13:   13    46     6     2     1
  14:   14     3     5    11    36     6    2   1
  15:   15    58     7    18     4     2    1
  16:   16     4     2     1
  17:   17    70     8     2     1
  18:   18     4     2     1
  19:   19    82     9    27   140    11   36   6   2   1
  20:   20     4     2     1
  21:   21    96     9    27   140    11   36   6   2   1
  22:   22     4     2     1
  23:   23   110    10     3     5    11   36   6   2   1
  24:   24     4     2     1
  25:   25   125  1397 52214   228    15   58   7  18   4   2   1

Prog

(Python)
import math
def row(n):
    if n==1: return [1]
    l=[n]
    while True:
        if n%2: n=math.isqrt(n**3)
        else:   n=math.isqrt(n)
        if n not in l:
            l+=[n]
            if n==1: break
        else:
            break
    return l
for n in range(1, 101): print(row(n))

Crossrefs

Cf. A094683 (Juggler sequence), A007320 (number of steps to reach 1), A094670, A094679.

Sequence in context: A092944 A384067 A049902 * A096631 A144057 A272891

Adjacent sequences: A389380 A389381 A389382 * A389384 A389385 A389386

Keyword

nonn,tabf

Author

Saeed Hatami Boura, Oct 02 2025

Status

approved