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A349576
Recurrence a(1) = 1, a(2) = 5; a(n) = (a(n-1) + a(n-2))/GCD(a(n-1),a(n-2)) + 1.
2
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
1,2
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.
PROG
(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
CROSSREFS
Sequence in context: A314329 A154872 A314330 * A022319 A207079 A167798
KEYWORD
nonn
AUTHOR
Peter Kagey, Dec 30 2021
STATUS
approved