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A365991
Square array read by ascending antidiagonals: T(n,k) is the k-th iterate of the 5x+1 function started at n, with n >= 1 and k >= 0.
5
1, 2, 3, 3, 1, 8, 4, 8, 3, 4, 5, 2, 4, 8, 2, 6, 13, 1, 2, 4, 1, 7, 3, 33, 3, 1, 2, 3, 8, 18, 8, 83, 8, 3, 1, 8, 9, 4, 9, 4, 208, 4, 8, 3, 4, 10, 23, 2, 23, 2, 104, 2, 4, 8, 2, 11, 5, 58, 1, 58, 1, 52, 1, 2, 4, 1, 12, 28, 13, 29, 3, 29, 3, 26, 3, 1, 2, 3
OFFSET
1,2
COMMENTS
The 5x+1 function (A185452), denoted by T_5(x) in the literature, is defined as T_5(x) = (5x+1)/2 if x is odd, T_5(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 ...
--------------------------------------------------------------------
1 | 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, ...
2 | 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, ...
3 | 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, ...
4 | 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, 2, ...
5 | 5, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, ...
6 | 6, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, ...
7 | 7, 18, 9, 23, 58, 29, 73, 183, 458, 229, 573, 1433, ...
8 | 8, 4, 2, 1, 3, 8, 4, 2, 1, 3, 8, 4, ...
9 | 9, 23, 58, 29, 73, 183, 458, 229, 573, 1433, 3583, 8958, ...
10 | 10, 5, 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, ...
11 | 11, 28, 14, 7, 18, 9, 23, 58, 29, 73, 183, 458, ...
12 | 12, 6, 3, 8, 4, 2, 1, 3, 8, 4, 2, 1, ...
13 | 13, 33, 83, 208, 104, 52, 26, 13, 33, 83, 208, 104, ...
14 | 14, 7, 18, 9, 23, 58, 29, 73, 183, 458, 229, 573, ...
15 | 15, 38, 19, 48, 24, 12, 6, 3, 8, 4, 2, 1, ...
...
MATHEMATICA
A365991list[dmax_]:=With[{a=Array[NestList[If[OddQ[#], (5#+1)/2, #/2]&, dmax-#, #]&, dmax, 0]}, Array[Diagonal[a, #]&, dmax, 1-dmax]]; A365991list[20] (* Generates 20 antidiagonals *)
CROSSREFS
Cf. A185452, A347270, A365484, A365992 (parity), A368301 (main diagonal).
Sequence in context: A236937 A323748 A116155 * A144149 A097005 A068008
KEYWORD
nonn,easy,tabl
AUTHOR
Paolo Xausa, Sep 25 2023
STATUS
approved