A393595 Sequence where k is appended after every k^k occurrences of 1, with multiple values following a 1 listed in order.

1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2

Offset

1,5

Comments

The frequencies of the terms follow the probability distribution given by pdf(k) = 1/(A073009*(k^k)).

The geometric mean approaches Product_{k>=1} k^(1/(A073009*(k^k))) = 1.185698... in the limit.

Links

Jwalin Bhatt, Table of n, a(n) for n = 1..10000

Formula

After every 4 ones we see a 2, after every 27 ones we see a 3 and so on.

Prog

(Python)
from itertools import islice
def power_distribution_generator():
    num_ones, num_reached = 0, 1
    while num_ones := num_ones+1:
        yield 1
        for num in range(2, num_reached+2):
            if num_ones % (num**num) == 0:
                yield num
                num_reached += num == num_reached+1
A393595 = list(islice(power_distribution_generator(), 120))

Crossrefs

Cf. A073009.

Sequence in context: A177706 A130782 A364358 * A055457 A277873 A032542

Adjacent sequences: A393592 A393593 A393594 * A393596 A393597 A393598

Keyword

nonn

Author

Jwalin Bhatt, Feb 23 2026

Status

approved