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

1,2

Comments

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

Links

Table of n, a(n) for n=1..75.

Rémy Sigrist, PARI program for A299962

Index entries for sequences related to 3x+1 (or Collatz) problem

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.

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A157524 A239496 A348164 * A340010 A128586 A130971

Adjacent sequences: A299959 A299960 A299961 * A299963 A299964 A299965

Keyword

nonn,tabl

Author

Rémy Sigrist, Feb 22 2018

Status

approved