A364090 Add each term m of the sequence to the last one m times starting with 1, 1.

1, 1, 2, 3, 5, 7, 10, 13, 16, 21, 26, 31, 36, 41, 48, 55, 62, 69, 76, 83, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 203, 216, 229, 242, 255, 268, 281, 294, 307, 320, 333, 346, 359, 375, 391, 407, 423, 439, 455, 471, 487, 503, 519, 535, 551, 567

Offset

1,3

Comments

a(n) seems to grow as n^c where c is a constant with the value of approximately 1.625, in other words, lim_{n->oo} log_n(a(n)) seems to converge.

Links

Table of n, a(n) for n=1..57.

Example

k denotes the k-th iteration
The sequence is initialized with (1, 1)
For k = 1
Add a(1) = 1 once, you get (1, 1, 2)
For k = 2
Add a(2) = 1 once, you get (1, 1, 2, 3)
For k = 3
Add a(3) = 2 twice, you get (1, 1, 2, 3, 5, 7)
For k = 4
add a(4) = 3 three times, and you get (1, 1, 2, 3, 5, 7, 10, 13, 16)

Prog

(Python)
def a_list(n):
    if n <= 2:
        return 1
    sequence = [1, 1]
    target_number_index = 0
    times_to_add = sequence[target_number_index]
    for _ in range(n - 2):
        if times_to_add == 0:
            target_number_index += 1
            times_to_add = sequence[target_number_index]
        last_term = sequence[-1]
        sequence.append(last_term + sequence[target_number_index])
        times_to_add -= 1
    return sequence

Crossrefs

Cf. A100143.

Sequence in context: A022790 A248360 A194238 * A270192 A053034 A029707

Adjacent sequences: A364087 A364088 A364089 * A364091 A364092 A364093

Keyword

easy,nonn

Author

Wagner Martins, Jul 09 2023

Status

approved