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

1,1

Links

Table of n, a(n) for n=1..78.

Formula

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

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}]

Prog

(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

Crossrefs

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

Cf. A090092, A090093.

Sequence in context: A113496 A343670 A086531 * A282176 A204918 A322999

Adjacent sequences: A089088 A089089 A089090 * A089092 A089093 A089094

Keyword

easy,nonn

Author

Labos Elemer, Nov 26 2003

Extensions

Offset corrected by Mohammed Yaseen, Aug 15 2023

Status

approved