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A365484
Square array read by ascending antidiagonals: T(n,k) is the k-th iterate of the 3x+1 function started at n, with n >= 1 and k >= 0.
5
1, 2, 2, 3, 1, 1, 4, 5, 2, 2, 5, 2, 8, 1, 1, 6, 8, 1, 4, 2, 2, 7, 3, 4, 2, 2, 1, 1, 8, 11, 5, 2, 1, 1, 2, 2, 9, 4, 17, 8, 1, 2, 2, 1, 1, 10, 14, 2, 26, 4, 2, 1, 1, 2, 2, 11, 5, 7, 1, 13, 2, 1, 2, 2, 1, 1, 12, 17, 8, 11, 2, 20, 1, 2, 1, 1, 2, 2, 13, 6, 26, 4, 17, 1, 10, 2, 1, 2, 2, 1, 1
OFFSET
1,2
COMMENTS
The 3x+1 function (A014682), denoted by T(x) in the literature, is defined as T(x) = (3x+1)/2 if x is odd, T(x) = x/2 if x is even.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..11325 (antidiagonals 1..150 of the array, flattened)
Alex V. Kontorovich and Jeffrey C. Lagarias, Stochastic Models for the 3x+1 and 5x+1 Problems, arXiv:0910.1944 [math.NT], 2009, and in Jeffrey C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, American Mathematical Society, 2010, pp. 131-188.
EXAMPLE
The array begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
--------------------------------------------------------------------
1 | 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
2 | 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
3 | 3, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
4 | 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
5 | 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
6 | 6, 3, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
7 | 7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, ...
8 | 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
9 | 9, 14, 7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, ...
10 | 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
11 | 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, ...
12 | 12, 6, 3, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
13 | 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
14 | 14, 7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, ...
15 | 15, 23, 35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 1, 2, 1, ...
...
MATHEMATICA
A365484list[dmax_]:=With[{a=Array[NestList[If[OddQ[#], (3#+1)/2, #/2]&, dmax-#, #]&, dmax, 0]}, Array[Diagonal[a, #]&, dmax, 1-dmax]]; A365484list[20] (* Generates 20 antidiagonals *)
CROSSREFS
Cf. A014682, A347270 (equivalent for the Collatz function), A365495 (parity), A365991, A368300 (main diagonal).
Sequence in context: A362749 A264010 A071435 * A335814 A119428 A241815
KEYWORD
nonn,easy,tabl
AUTHOR
Paolo Xausa, Sep 06 2023
STATUS
approved