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A350279 Irregular triangle T(n,k) read by rows in which row n lists the iterates of the Farkas map (A349407) from 2*n - 1 to 1.

%I A350279 #22 Sep 13 2024 08:11:16
%S A350279 1,3,1,5,3,1,7,11,17,9,3,1,9,3,1,11,17,9,3,1,13,7,11,17,9,3,1,15,5,3,
%T A350279 1,17,9,3,1,19,29,15,5,3,1,21,7,11,17,9,3,1,23,35,53,27,9,3,1,25,13,7,
%U A350279 11,17,9,3,1,27,9,3,1,29,15,5,3,1
%N A350279 Irregular triangle T(n,k) read by rows in which row n lists the iterates of the Farkas map (A349407) from 2*n - 1 to 1.
%H A350279 Paolo Xausa, <a href="/A350279/b350279.txt">Table of n, a(n) for n = 1..12301</a> (rows 1..1000 of triangle, flattened).
%H A350279 H. M. Farkas, "Variants of the 3N+1 Conjecture and Multiplicative Semigroups", in Entov, Pinchover and Sageev, <a href="https://bookstore.ams.org/conm-387">Geometry, Spectral Theory, Groups, and Dynamics, Contemporary Mathematics, vol. 387</a>, American Mathematical Society, 2005, p. 121.
%H A350279 J. 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, p. 74.
%F A350279 T(n,1) = 2*n-1; T(n,k) = A349407((T(n,k-1)+1)/2), where n >= 1 and k >= 2.
%e A350279 Written as an irregular triangle, the sequence begins:
%e A350279   n\k   1   2   3   4   5   6   7
%e A350279   -------------------------------
%e A350279    1:   1
%e A350279    2:   3   1
%e A350279    3:   5   3   1
%e A350279    4:   7  11  17   9   3   1
%e A350279    5:   9   3   1
%e A350279    6:  11  17   9   3   1
%e A350279    7:  13   7  11  17   9   3   1
%e A350279    8:  15   5   3   1
%e A350279    9:  17   9   3   1
%e A350279   10:  19  29  15   5   3   1
%e A350279   11:  21   7  11  17   9   3   1
%e A350279   12:  23  35  53  27   9   3   1
%t A350279 FarkasStep[x_] := Which[Divisible[x, 3], x/3, Mod[x, 4] == 3, (3*x + 1)/2, True, (x + 1)/2];
%t A350279 Array[Most[FixedPointList[FarkasStep, 2*# - 1]] &, 15] (* _Paolo Xausa_, Sep 03 2024 *)
%Y A350279 Cf. A349407, A375909 (# of iterations), A375910 (row sums), A375911 (row maxs).
%Y A350279 Cf. A070165.
%K A350279 nonn,easy,tabf
%O A350279 1,2
%A A350279 _Paolo Xausa_, Dec 22 2021