A113496 a(n) = smallest composite integer > c(n) and coprime to c(n), where c(n) is the n-th composite integer.

9, 25, 9, 10, 21, 25, 15, 16, 21, 25, 21, 22, 25, 25, 26, 27, 28, 33, 49, 33, 34, 35, 36, 49, 39, 40, 49, 55, 45, 46, 49, 49, 50, 51, 52, 55, 55, 56, 57, 58, 63, 77, 63, 64, 65, 66, 85, 69, 70, 81, 77, 75, 76, 77, 78, 85, 81, 82, 85, 85, 86, 87, 88, 91, 91, 92, 93, 94, 95, 96

Offset: 1

Author

Leroy Quet, Jan 11 2006

Keywords

• nonn

Crossrefs

Cf. A002808, A113484.

Programs

Mathematica

Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; f[n_] := Block[{k = n + 1}, While[PrimeQ@k || GCD[k, n] > 1, k++ ]; k]; Array[ f[ Composite[ # ]] &, 70] (* Robert G. Wilson v, Jan 12 2006 *)

Python

from sympy import isprime, gcd, composite
def A113496(n):
    m = composite(n)
    k = m+1
    while gcd(k,m) != 1 or isprime(k):
        k += 1
    return k # Chai Wah Wu, Mar 28 2021

Formula

a(n) = A113484(A002808(n)). - Robert G. Wilson v, Jan 12 2006

Extensions

More terms from Robert G. Wilson v, Jan 12 2006