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

Author

Markus Sigg, Sep 03 2024

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A033496, A176869.

Programs

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)));

Formula

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