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A347271
Irregular triangle T(n,k) read by rows in which row n lists the terms of the 3x+1 trajectory of n, but the row ends when a term is a power of 2 or when a term is less than n, with n >= 1 and k >= 0.
1
1, 2, 3, 10, 5, 16, 4, 5, 16, 6, 3, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 8, 9, 28, 14, 7, 10, 5, 11, 34, 17, 52, 26, 13, 40, 20, 10, 12, 6, 13, 40, 20, 10, 14, 7, 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 16, 17, 52, 26, 13, 18, 9, 19, 58, 29, 88, 44, 22, 11
OFFSET
1,2
COMMENTS
Note that every row ends when it is easy to know the next missing terms because they are powers of 2 or the last term and the next missing terms form a row that it is already in the sequence.
For a square array with infinitely many terms in every row, see A347270, which is a supersequence that contains all 3x+1 sequences.
EXAMPLE
Triangle begins:
1;
2;
3, 10, 5, 16;
4;
5, 16;
6, 3;
7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5;
8;
9, 28, 14, 7;
10, 5;
11, 34, 17, 52, 26, 13, 40, 20, 10;
12, 6;
13, 40, 20, 10;
14, 7;
15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10;
16;
17, 52, 26, 13;
18, 9;
19, 58, 29, 88, 44, 22, 11;
...
For n = 3 the 3x+1 trajectory is 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, ... The fourth term is 16 which is a power of 2 so the third row of the triangle is [3, 10, 5, 16].
For n = 6 the 3x+1 trajectory is 6, 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, ... The second term is 3 which is less than 6 so the 6th row of the triangle is [6, 3].
CROSSREFS
Subsequence of A070165, of A235795 and of A347270.
Sequence in context: A112417 A139693 A182076 * A266552 A263716 A344457
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Aug 25 2021
STATUS
approved