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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
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 (list; table; graph; refs; listen; history; text; internal format)
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: A055377 A157524 A239496 * A128586 A130971 A051776

Adjacent sequences:  A299959 A299960 A299961 * A299963 A299964 A299965

KEYWORD

nonn,tabl

AUTHOR

Rémy Sigrist, Feb 22 2018

STATUS

approved

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Last modified December 8 01:34 EST 2019. Contains 329850 sequences. (Running on oeis4.)