A113484 a(n) = smallest composite integer > n and coprime to n.

4, 9, 4, 9, 6, 25, 8, 9, 10, 21, 12, 25, 14, 15, 16, 21, 18, 25, 20, 21, 22, 25, 24, 25, 26, 27, 28, 33, 30, 49, 32, 33, 34, 35, 36, 49, 38, 39, 40, 49, 42, 55, 44, 45, 46, 49, 48, 49, 50, 51, 52, 55, 54, 55, 56, 57, 58, 63, 60, 77, 62, 63, 64, 65, 66, 85, 68, 69, 70, 81, 72, 77

Offset: 1

Author

Leroy Quet, Jan 11 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A113496.

Programs

Mathematica

f[n_] := Block[{k = n + 1}, While[PrimeQ@k || GCD[k, n] > 1, k++ ]; k]; Array[f, 72] (* Robert G. Wilson v *)

PARI

a(n) = my(k = n+1); while(isprime(k) || (gcd(n,k) != 1), k++); k; \\ Michel Marcus, Mar 13 2017

Python

from sympy import isprime, gcd
def A113484(n):
    k = n+1
    while gcd(k,n) != 1 or isprime(k):
        k += 1
    return k # Chai Wah Wu, Mar 28 2021

Formula

a(p) = p+1 for prime p > 2. - Michel Marcus, Mar 13 2017

Extensions

More terms from Robert G. Wilson v, Jan 13 2006