A299962 Square array T(n, k) read by antidiagonals upwards, n > 0 and k > 0: T(n, k) is the k-th positive number whose Collatz sequence contains n.

1, 2, 2, 3, 3, 3, 3, 6, 4, 4, 3, 4, 12, 5, 5, 6, 5, 5, 24, 6, 6, 7, 12, 6, 6, 48, 7, 7, 3, 9, 24, 7, 7, 96, 8, 8, 9, 5, 14, 48, 9, 8, 192, 9, 9, 3, 18, 6, 18, 96, 10, 9, 384, 10, 10, 7, 6, 36, 7, 28, 192, 11, 10, 768, 11, 11, 12, 9, 7, 72, 8, 36, 384, 12, 11

Offset: 1

Author

Rémy Sigrist, Feb 22 2018

Keywords

• nonn
• tabl

Comments

The n-th row corresponds to indices of rows in A070165 containing n.

Examples

			Array T(n, k) begins:
  n\k|  1     2     3     4     5     6     7     8     9    10
  ---+---------------------------------------------------------
    1|  1     2     3     4     5     6     7     8     9    10  -->  A000027 ?
    2|  2     3     4     5     6     7     8     9    10    11
    3|  3     6    12    24    48    96   192   384   768  1536  -->  A007283
    4|  3     4     5     6     7     8     9    10    11    12
    5|  3     5     6     7     9    10    11    12    13    14
    6|  6    12    24    48    96   192   384   768  1536  3072  -->  A091629
    7|  7     9    14    18    28    36    37    43    49    56
    8|  3     5     6     7     8     9    10    11    12    13
    9|  9    18    36    72   144   288   576  1152  2304  4608
   10|  3     6     7     9    10    11    12    13    14    15
		

Links

• Rémy Sigrist, PARI program for A299962
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A000027, A007283, A091629, A070165, A070167.

Programs

PARI

See Links section.

Formula

T(n, 1) = A070167(n) for any n > 0.

T(3*n, k) = 3*n * 2^(k-1) for any n > 0 and k > 0.

If the Collatz conjecture is true, then:

- T(1, k) = k for any k > 0,

- T(2, k) = k+1 for any k > 0.