A375937 Odd numbers which are the largest odd number in their Collatz trajectory.

1, 5, 13, 17, 21, 29, 33, 37, 45, 49, 53, 61, 65, 69, 77, 81, 85, 93, 101, 113, 117, 133, 141, 149, 157, 173, 177, 181, 197, 205, 209, 213, 229, 237, 241, 245, 261, 269, 273, 277, 289, 301, 305, 309, 317, 321, 325, 341, 349, 357, 369, 373, 385, 397, 401, 405

Offset

1,2

Comments

a(n) == 1 (mod 4) because the trajectory of 4x+3 is (4x+3, 12x+10, 6x+5, ...) and 6x+5 > 4x+3.

Links

Markus Sigg, Table of n, a(n) for n = 1..10000

Formula

a(n) = (A176869(n) - 1) / 3 for n > 1.

Example

The odd elements of the Collatz trajectory (3,10,5,16,8,4,2,1) are {3,5,1} with maximum 5 > 3, so 3 is not a term. The odd elements of the Collatz trajectory (13,40,20,10,5,16,8,4,2,1) are {13,5,1} with maximum 13, so 13 is a term.

Prog

(PARI)
makeEntries(count) = {
    my(L = List(), k = 1);
    while(#L < count,
        my(m = k);
        while(m > 1 && m <= k,
            m = 3*m + 1;
            while(m % 2 == 0, m = m / 2);
        );
        if(m == 1, listput(L, k));
        k += 2
    );
    L
};
print(Vec(makeEntries(56)));

Crossrefs

Cf. A033496, A176869.

Sequence in context: A166409 A077425 A039955 * A213340 A014539 A249034

Adjacent sequences: A375934 A375935 A375936 * A375938 A375939 A375940

Keyword

nonn

Author

Markus Sigg, Sep 03 2024

Status

approved