A355914 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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.