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%I #25 Dec 21 2023 05:25:18
%S 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,
%T 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,
%U 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
%N 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.
%C 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.
%H Paolo Xausa, <a href="/A365484/b365484.txt">Table of n, a(n) for n = 1..11325</a> (antidiagonals 1..150 of the array, flattened)
%H Alex V. Kontorovich and Jeffrey C. Lagarias, <a href="https://arxiv.org/abs/0910.1944">Stochastic Models for the 3x+1 and 5x+1 Problems</a>, arXiv:0910.1944 [math.NT], 2009, and in Jeffrey C. Lagarias, ed., <a href="http://www.ams.org/bookstore-getitem/item=mbk-78">The Ultimate Challenge: The 3x+1 Problem</a>, American Mathematical Society, 2010, pp. 131-188.
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e The array begins:
%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
%e --------------------------------------------------------------------
%e 1 | 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
%e 2 | 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
%e 3 | 3, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
%e 4 | 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
%e 5 | 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
%e 6 | 6, 3, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ...
%e 7 | 7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, ...
%e 8 | 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
%e 9 | 9, 14, 7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, ...
%e 10 | 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
%e 11 | 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, ...
%e 12 | 12, 6, 3, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
%e 13 | 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...
%e 14 | 14, 7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, ...
%e 15 | 15, 23, 35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 1, 2, 1, ...
%e ...
%t 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 *)
%Y Cf. A014682, A347270 (equivalent for the Collatz function), A365495 (parity), A365991, A368300 (main diagonal).
%K nonn,easy,tabl
%O 1,2
%A _Paolo Xausa_, Sep 06 2023
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