A089091 a(n) is the smallest composite number coprime to n and n+1.

9, 25, 25, 9, 49, 25, 9, 25, 49, 9, 25, 25, 9, 121, 49, 9, 25, 25, 9, 121, 25, 9, 25, 49, 9, 25, 25, 9, 49, 49, 9, 25, 25, 9, 121, 25, 9, 25, 49, 9, 25, 25, 9, 49, 49, 9, 25, 25, 9, 49, 25, 9, 25, 49, 9, 25, 25, 9, 49, 49, 9, 25, 25, 9, 49, 25, 9, 25, 121, 9, 25, 25, 9, 49, 49, 9, 25, 25

Offset: 1

Author

Labos Elemer, Nov 26 2003

Keywords

• easy
• nonn

Crossrefs

Cf. A007978, A053669, A053670, A053671, A053672, A053673, A053674.

Cf. A090092, A090093.

Programs

Mathematica

m=0;Table[fla=1;Do[s=GCD[n, k]; s1=GCD[n, k+1];s2=GCD[n, k+2];s3=GCD[n, k+3]; If[Equal[s, 1]&&Equal[s1, 1]&&!PrimeQ[n]&&!Equal[n, 1]&& Equal[fla, 1], m=m+1;Print[n];fla=0], {n, 1, 1000}], {k, 1, 256}]

Python

from math import gcd
def a(n):
    k, m = 3, n*(n+1)
    while gcd(k, m) != 1: k += 2
    return k*k
print([a(n) for n in range(1, 79)]) # Michael S. Branicky, Sep 25 2021

Formula

a(n) = A053670(n)^2.

Extensions

Offset corrected by Mohammed Yaseen, Aug 15 2023