A381900 Sequence where k is appended after every (2^(k-1))*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, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 5

Offset

1,5

Comments

The frequencies of the terms follow the logarithmic distribution with parameter value 1/2.

The geometric mean approaches A381898 in the limit.

Links

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

Wikipedia, Logarithmic distribution

Example

After every (2*2=4) ones we see a 2,
after every (4*3=12) ones we see a 3,
after every (8*4=32) ones we see a 4 and so on.

Prog

(Python)
from itertools import islice
def logarithmic_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 % ((2**(num-1))*(num)) == 0:
                yield num
                num_reached += num == num_reached+1
A381900 = list(islice(logarithmic_distribution_generator(), 120))

Crossrefs

Cf. A381522, A381898.

Sequence in context: A025896 A050432 A343747 * A334925 A247090 A030346

Adjacent sequences: A381897 A381898 A381899 * A381901 A381902 A381903

Keyword

nonn

Author

Jwalin Bhatt, Mar 09 2025

Status

approved