A349576 Recurrence a(1) = 1, a(2) = 5; a(n) = (a(n-1) + a(n-2))/GCD(a(n-1),a(n-2)) + 1.

1, 5, 7, 13, 21, 35, 9, 45, 7, 53, 61, 115, 177, 293, 471, 765, 413, 1179, 1593, 309, 635, 945, 317, 1263, 1581, 949, 2531, 3481, 6013, 9495, 15509, 25005, 40515, 4369, 44885, 49255, 18829, 68085, 86915, 31001, 117917, 148919, 266837, 415757, 682595, 1098353

Offset: 1

Author

Peter Kagey, Dec 30 2021

Keywords

• nonn

Comments

Conjecture: this sequence is not periodic. (Note that the analogous sequences with a(2) = 1, 2, 3, or 4 are periodic.)

Links

• Mathematics Stack Exchange user Augusto Santi, Investigating the recurrence relation.

Programs

Python

from itertools import islice
from math import gcd
def A349576_gen(): # generator of terms
    blist = [1, 5]
    yield from blist
    while True:
        blist = [blist[1],sum(blist)//gcd(*blist) + 1]
        yield blist[-1]
A349576_list = list(islice(A349576_gen(),30)) # Chai Wah Wu, Jan 10 2022