A383855 The n-th term of the sequence is k after every k*(k+1)/2 occurrences of 1, with multiple values following a 1 listed in order.

1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 1, 4, 1, 1, 2, 3, 1, 1, 1, 2, 5, 1, 1, 1, 2, 3, 1, 1, 4, 1, 2, 6, 1, 1, 1, 2, 3, 1, 1, 1, 2, 1, 7, 1, 1, 2, 3, 4, 5, 1, 1, 1, 2, 1, 1, 1, 2, 3, 8, 1, 1, 1, 2, 1, 4, 1, 1, 2, 3, 6, 1, 1, 1, 2, 5, 9, 1, 1, 1, 2, 3, 1, 1, 4, 1, 2, 1, 1, 1, 2, 3, 1, 10

Offset

1,4

Comments

The frequencies of the terms follow the Yule-Simon distribution with parameter value 1. The geometric mean approaches A245254 in the limit.

Links

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

Wikipedia, Yule-Simon distribution

Example

After every ((2*3)/2=3) ones we see a 2,
after every ((3*4)/2=6) ones we see a 3,
after every ((4*5)/2=10) ones we see a 4 and so on.

Prog

(Python)
from itertools import islice
def beta_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+1)//2) == 0:
                yield num
                num_reached += num == num_reached+1
A383855 = list(islice(beta_distribution_generator(), 120))

Crossrefs

Cf. A245254, A383899.

Sequence in context: A245563 A356917 A122945 * A209972 A205573 A119338

Adjacent sequences: A383852 A383853 A383854 * A383856 A383857 A383858

Keyword

nonn

Author

Jwalin Bhatt, May 12 2025

Status

approved