A335296 Least index a(n) such that the sequences b(n,m) from A334539 are purely periodic after a(n).

1, 1, 1, 1, 1, 1, 16, 24, 70, 31, 98, 112, 116, 170, 216, 488, 2012, 795, 328, 219, 2993, 4486, 1555, 814, 3575, 12296, 18386, 29659, 13665, 2162, 47685, 52346, 69061, 447927, 472933, 33798, 857812, 179171, 47447, 1195784, 332172, 618783, 248092, 3947618, 2718980, 15924182, 2857983, 3536883, 8606700

Offset

1,7

Comments

By the pigeonhole principle, a(n) is upper bounded by n^n - n.

Links

Elad Michael, Table of n, a(n) for n = 1..100

Reddit user supermac30, Foggy Sequences.

Example

The sequence b(3, m) is 1, 1, 2, 1, 2, 2, 2, 3, 1, 1, 2, ... which is periodic at index 1 with period 8.
The sequence b(8, m) is 1, 1, 2, 1, 3, 1, 4, ... 3, 4, 1, 2, 3, 3, 4, 2, 2, 3, 3, 4, 2, 3, 3, 4, 2, 2, 3, 3, ... which is periodic at index 24 with period 9.

Prog

(Python)
def a(n):
    b = [1];
    for i in range(2, n+1):
        b.append(b.count(b[-1]));
    prev = {tuple(b):1};
    m = 1;
    while(True):
        b.append(b.count(b[-1]));
        del b[0];
        m += 1;
        if(tuple(b) in prev):
            return prev[tuple(b)]
        else:
            prev[tuple(b)] = m;

Crossrefs

Cf. A334539.

Sequence in context: A204696 A024588 A334229 * A358447 A120468 A166629

Adjacent sequences: A335293 A335294 A335295 * A335297 A335298 A335299

Keyword

nonn

Author

Elad Michael, May 30 2020

Status

approved