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.
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
KEYWORD
easy,nonn
AUTHOR
Wagner Martins, Jul 09 2023
STATUS
approved