A355914 a(n) = gcd(b(n-1),b(n)), where b(n) = A351871(n).

1, 2, 1, 5, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 8, 2, 3, 3, 6, 1, 1, 6, 1, 1, 6, 10, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 30, 5, 5, 8, 1, 1, 4, 43, 1, 2, 1, 3, 4, 1, 3, 12, 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 25, 1, 4, 1, 1, 6, 1, 1, 6

Offset

2,2

Comments

In order to understand the difference between A351871 (which cycles) and A355898 (which appears to diverge), it would be helpful to understand the difference between the respective gcd sequences (this and A355899 - the latter has a very interesting graph!).

Links

Michael S. Branicky, Table of n, a(n) for n = 2..10001

Prog

(Python)
from math import gcd
from itertools import islice
def agen():
    a = [1, 2]
    while True: g = gcd(*a); yield g; a = [a[-1], g + sum(a)//g]
print(list(islice(agen(), 85))) # Michael S. Branicky, Sep 19 2022

Crossrefs

Cf. A351871, A355898, A355899.

Sequence in context: A140879 A006556 A108790 * A117941 A134566 A128694

Adjacent sequences: A355911 A355912 A355913 * A355915 A355916 A355917

Keyword

nonn

Author

N. J. A. Sloane, Sep 19 2022

Extensions

a(66) and beyond from Michael S. Branicky, Sep 19 2022

Status

approved