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.

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, 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, 16, 4, 16, 16, 52, 8, 52, 16, 52, 1, 2, 16, 4, 16, 16, 16, 8, 16, 16, 16, 16

Offset: 1

Author

Markus Sigg, Sep 03 2024

Keywords

• nonn
• tabl

Examples

			The triangle begins:
       k=1  2   3  4   5   6    7  8
  n=1:   1;
  n=2:   1, 2;
  n=3:   1, 2, 16;
  n=4:   1, 2,  4, 4;
  n=5:   1, 2, 16, 4, 16;
  n=6:   1, 2, 16, 4, 16, 16;
  n=7:   1, 2, 16, 4, 16, 16, 52;
  n=8:   1, 2,  8, 4,  8,  8,  8, 8;
  ...
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.
		

Links

• Markus Sigg, Table of n, a(n) for n = 1..11325 (row 1..150).

Crossrefs

Cf. A025586 (main diagonal)

Programs

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);
a375955_row(n) = my(Cn = C(n)); vector(n, k, vecmax(setintersect(Cn, C(k))));

Formula

T(n,n) = A025586(n).