%I #21 Oct 15 2022 21:16:10

%S 7,13,7,31,43,19,73,13,37,19,157,61,211,241,1,307,1,127,421,463,1,79,

%T 601,31,37,757,271,67,1,331,151,1123,397,97,43,67,1483,223,547,1723,

%U 139,631,283,109,103,61,181,1,2551,379,919,409,2971,79,103,3307,163,3541,523,97,3907,109,73,613

%N a(n) = A081257(n) if A081257(n) > n, otherwise a(n) = 1.

%C All the primes in this sequence appear exactly twice.

%C The new primes encountered seem to match the terms of A256148 for n>1. _Bill McEachen_, Oct 13 2022

%F Conjecture 1: If a(n) != 1, then a(n) = a(a(n) - n - 1).

%F Conjecture 2: If n != m and a(n) = a(m), then

%F a(n) = gcd(n^2 + n + 1, m^2 + m + 1) = n + m + 1.

%e a(2) = a(a(2) - 2 - 1) = a(7 - 2 - 1) = a(4).

%e a(3) = a(9) = 3 + 9 + 1 = 13.

%e a(5) = a(25) = gcd(5^2 + 5 + 1, 25^2 + 25 + 1) = 31.

%o (Python)

%o from sympy import primefactors

%o def A357127(n): return m if (m:=max(primefactors(n*(n+1)+1))) > n else 1 # _Chai Wah Wu_, Oct 15 2022

%Y Cf. A081257, A081256, A108768, A256148.

%K nonn

%O 2,1

%A _Mohammed Bouras_, Sep 13 2022