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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
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
2,2
COMMENTS
The restriction k < n is there to avoid the trivial values T(n,n) = 0. Consequently, the first term is T(2,1).
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.
EXAMPLE
The triangle begins
1,
7, 6,
2, 1, 5,
5, 4, 2, 3,
8, 7, 1, 6, 3,
...
PROG
(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))
)
)
};
CROSSREFS
KEYWORD
tabl,nonn
AUTHOR
Markus Sigg, Oct 16 2024
STATUS
approved