A375206 T(n,k) for n >= 2, k < n is the distance of n and k in the Collatz graph, where T(n,k) is a triangle read by rows.

1, 7, 6, 2, 1, 5, 5, 4, 2, 3, 8, 7, 1, 6, 3, 16, 15, 11, 14, 11, 12, 3, 2, 4, 1, 2, 5, 13, 19, 18, 14, 17, 14, 15, 3, 16, 6, 5, 1, 4, 1, 2, 10, 3, 13, 14, 13, 9, 12, 9, 10, 2, 11, 5, 8, 9, 8, 2, 7, 4, 1, 13, 6, 16, 3, 11, 9, 8, 4, 7, 4, 5, 7, 6, 10, 3, 5, 6, 17, 16, 12, 15, 12, 13, 1, 14, 2, 11, 3, 14, 8, 17, 16, 12, 15, 12, 13, 17, 14, 20, 11, 15, 14, 10, 18

Offset: 2

Author

Markus Sigg, Oct 16 2024

Keywords

• tabl
• nonn

Comments

The restriction k < n is there to avoid the trivial values T(n,n) = 0. Consequently, the first term is T(2,1).

Examples

			The triangle begins
  1,
  7, 6,
  2, 1, 5,
  5, 4, 2, 3,
  8, 7, 1, 6, 3,
  ...
		

Links

• Markus Sigg, Table of n, a(n) for n = 2..10012 (rows 2..142, flattened)
• Hugo Pfoertner, Animated 3-d view of rows 2..200, view angle tilted by 15 degrees against the n-k plane, 2024.

Crossrefs

Cf. A006370, A008908, A070165.

Programs

PARI

C(n) = {
    my(L = List([n]));
    while(n > 1, n = if(n % 2 == 0, n/2, 3*n+1); listput(L, n));
    L
};
a375206(n,k) = {
    my(Cn = C(n), Ck = C(k));
    for(i = 1, #Cn,
        for(j = 1, #Ck,
            if(Cn[i] == Ck[j], return(i+j-2))
        )
    )
};