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A375955 T(n,k) for n >= 1, k <= n is the maximum value in the intersection of the Collatz trajectories of n and k, where a trajectory ends when it reaches 1. T(n,k) is a triangle read by rows.

%I A375955 #29 Sep 07 2024 16:30:45
%S A375955 1,1,2,1,2,16,1,2,4,4,1,2,16,4,16,1,2,16,4,16,16,1,2,16,4,16,16,52,1,
%T A375955 2,8,4,8,8,8,8,1,2,16,4,16,16,52,8,52,1,2,16,4,16,16,16,8,16,16,1,2,
%U A375955 16,4,16,16,52,8,52,16,52,1,2,16,4,16,16,16,8,16,16,16,16
%N A375955 T(n,k) for n >= 1, k <= n is the maximum value in the intersection of the Collatz trajectories of n and k, where a trajectory ends when it reaches 1. T(n,k) is a triangle read by rows.
%H A375955 Markus Sigg, <a href="/A375955/b375955.txt">Table of n, a(n) for n = 1..11325</a> (row 1..150).
%F A375955 T(n,n) = A025586(n).
%e A375955 The triangle begins:
%e A375955        k=1  2   3  4   5   6    7  8
%e A375955   n=1:   1;
%e A375955   n=2:   1, 2;
%e A375955   n=3:   1, 2, 16;
%e A375955   n=4:   1, 2,  4, 4;
%e A375955   n=5:   1, 2, 16, 4, 16;
%e A375955   n=6:   1, 2, 16, 4, 16, 16;
%e A375955   n=7:   1, 2, 16, 4, 16, 16, 52;
%e A375955   n=8:   1, 2,  8, 4,  8,  8,  8, 8;
%e A375955   ...
%e A375955 T(20,3) = 16 since the trajectory of 20 is (20,10,5,16,8,4,2,1), the trajectory of 3 is (3,10,5,16,8,4,2,1), and their intersection has the maximum 16. This example shows that T(n,k) does not necessarily denote the start of the common trajectory of n and k.
%o A375955 (PARI) C(n) = my(L = List([n])); while(n > 1, n = if(n % 2 == 0, n/2, 3*n + 1); listput(L, n)); Set(L);
%o A375955 a375955_row(n) = my(Cn = C(n)); vector(n, k, vecmax(setintersect(Cn, C(k))));
%Y A375955 Cf. A025586 (main diagonal)
%K A375955 nonn,tabl
%O A375955 1,3
%A A375955 _Markus Sigg_, Sep 03 2024