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

Author

N. J. A. Sloane, Sep 19 2022

Keywords

• nonn

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

Crossrefs

Cf. A351871, A355898, A355899.

Programs

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

Extensions

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