A362296 Greatest common divisor of composite numbers between the n-th and (n+1)st primes.

4, 6, 1, 12, 1, 18, 1, 1, 30, 1, 1, 42, 1, 1, 1, 60, 1, 1, 72, 1, 1, 1, 1, 1, 102, 1, 108, 1, 1, 1, 1, 138, 1, 150, 1, 1, 1, 1, 1, 180, 1, 192, 1, 198, 1, 1, 1, 228, 1, 1, 240, 1, 1, 1, 1, 270, 1, 1, 282, 1, 1, 1, 312, 1, 1, 1, 1, 348, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 2

Author

Chai Wah Wu, Apr 15 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A056831 (LCM), A061214 (product).

Programs

PARI

a(n) = gcd([prime(n)+1..prime(n+1)-1]); \\ Michel Marcus, Apr 16 2023

Python

from sympy import prime, isprime
def A362296(n): return m-1 if isprime(m:=prime(n)+2) else 1

Formula

For n > 1, a(n)=prime(n)+1 if and only if prime(n+1)=prime(n)+2 and a(n)=1 otherwise.