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A288251 k-th term of n in the 3x+1 problem, k >= 1. Square array A(n, k) read by antidiagonals downwards. 0
4, 2, 1, 1, 4, 10, 4, 2, 5, 2, 2, 1, 16, 1, 16, 1, 4, 8, 4, 8, 3, 4, 2, 4, 2, 4, 10, 22, 2, 1, 2, 1, 2, 5, 11, 4, 1, 4, 1, 4, 1, 16, 34, 2, 28, 4, 2, 4, 2, 4, 8, 17, 1, 14, 5, 2, 1, 2, 1, 2, 4, 52, 4, 7, 16, 34, 1, 4, 1, 4, 1, 2, 26, 2, 22, 8, 17, 6, 4, 2, 4 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..81.

Wikipedia, Collatz conjecture

Index entries for sequences related to 3x+1 problem

FORMULA

T(m, n) = A(n, m-n+1), 1 <= n <= m, with A(n, k) = C^{[k]}(n), n >= 1, k >= 1, with iterations of the Collatz map C: n -> 3*n+1 if n is odd and n -> n/2 if n is even. - Wolfdieter Lang, Jul 13 2017

EXAMPLE

The array A(n, k) starts:

n\k |  1  2  3  4  5  6  7  8  9 10 11 12 ...

---------------------------------------------

1   |  4  2  1  4  2  1  4  2  1  4  2  1

2   |  1  4  2  1  4  2  1  4  2  1  4  2

3   | 10  5 16  8  4  2  1  4  2  1  4  2

4   |  2  1  4  2  1  4  2  1  4  2  1  4

5   | 16  8  4  2  1  4  2  1  4  2  1  4

6   |  3 10  5 16  8  4  2  1  4  2  1  4

7   | 22 11 34 17 52 26 13 40 20 10  5 16

8   |  4  2  1  4  2  1  4  2  1  4  2  1

9   | 28 14  7 22 11 34 17 52 26 13 40 20

10  |  5 16  8  4  2  1  4  2  1  4  2  1

...

The triangle T(m, n) starts:

m\n |  1 2  3 4  5  6  7 8  9 10 ...

------------------------------------

1   |  4

2   |  2 1

3   |  1 4 10

4   |  4 2  5 2

5   |  2 1 16 1 16

6   |  1 4  8 4  8  3

7   |  4 2  4 2  4 10 22

8   |  2 1  2 1  2  5 11 4

9   |  1 4  1 4  1 16 34 2 28

10  |  4 2  4 2  4  8 17 1 14  5

... formatted, Wolfdieter Lang, Jul 13 2017

PROG

(PARI) trajectory(n, terms) = my(i=0, x=n); while(1, if(x%2==0, x=x/2, x=3*x+1); print1(x, ", "); i++; if(i==terms, break))

array(n, k) = for(x=1, n, trajectory(x, k); print(""))

array(10, 12) \\ print initial 10 rows and 12 columns of array

CROSSREFS

Rows of A (columns of T): A153727 (row 1), A033478 (row 3), A033479 (row 9).

Columns of A (diagonals of T): A006370 (column 1), A075884 (column 2), A076536 (column 3).

Sequence in context: A051149 A293424 A152145 * A051758 A024553 A051568

Adjacent sequences:  A288248 A288249 A288250 * A288252 A288253 A288254

KEYWORD

nonn,easy,tabl

AUTHOR

Felix Fröhlich, Jun 10 2017

STATUS

approved

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Last modified June 17 18:57 EDT 2019. Contains 324198 sequences. (Running on oeis4.)