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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
OFFSET
1,2
COMMENTS
The n-th row corresponds to indices of rows in A070165 containing n.
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
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Feb 22 2018
STATUS
approved