A357127 a(n) = A081257(n) if A081257(n) > n, otherwise a(n) = 1.

7, 13, 7, 31, 43, 19, 73, 13, 37, 19, 157, 61, 211, 241, 1, 307, 1, 127, 421, 463, 1, 79, 601, 31, 37, 757, 271, 67, 1, 331, 151, 1123, 397, 97, 43, 67, 1483, 223, 547, 1723, 139, 631, 283, 109, 103, 61, 181, 1, 2551, 379, 919, 409, 2971, 79, 103, 3307, 163, 3541, 523, 97, 3907, 109, 73, 613

Offset: 2

Author

Mohammed Bouras, Sep 13 2022

Keywords

• nonn

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

Examples

			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.
		

Crossrefs

Cf. A081257, A081256, A108768, A256148.

Programs

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

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.