A375955 - OEIS

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

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OFFSET

1,3

LINKS

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

FORMULA

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

EXAMPLE

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.

PROG

(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))));

CROSSREFS

Cf. A025586 (main diagonal)

Sequence in context: A242085 A007402 A334505 * A251731 A058260 A202410

Adjacent sequences: A375952 A375953 A375954 * A375956 A375957 A375958

KEYWORD

nonn,tabl

AUTHOR

Markus Sigg, Sep 03 2024

STATUS

approved