OFFSET
2,1
COMMENTS
All the primes in this sequence appear exactly twice.
The new primes encountered seem to match the terms of A256148 for n>1. Bill McEachen, Oct 13 2022
FORMULA
Conjecture 1: If a(n) != 1, then a(n) = a(a(n) - n - 1).
Conjecture 2: If n != m and a(n) = a(m), then
a(n) = gcd(n^2 + n + 1, m^2 + m + 1) = n + m + 1.
EXAMPLE
a(2) = a(a(2) - 2 - 1) = a(7 - 2 - 1) = a(4).
a(3) = a(9) = 3 + 9 + 1 = 13.
a(5) = a(25) = gcd(5^2 + 5 + 1, 25^2 + 25 + 1) = 31.
PROG
(Python)
from sympy import primefactors
def A357127(n): return m if (m:=max(primefactors(n*(n+1)+1))) > n else 1 # Chai Wah Wu, Oct 15 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Mohammed Bouras, Sep 13 2022
STATUS
approved