A053674 -id:A053674 - cp's OEIS frontend

A190911 Least number coprime to n and n+3.

3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 11, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 11, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3

Offset: 1

Jonathan Vos Post, May 26 2011

This is to n+3 as A053670 is to n+1. This is the 3rd row of the array A(k,n) = Least number coprime to n and n+k where A053670 is the 1st row. First n for which a(n) = (3, 5, 7, 11, 13, 17, 19, ...) are A191112 = (1, 3, 12, 42, 165, 3000, 2142, ...).

			a(12) = 7 because the prime factors of 12 and 12+3 = 15 are {2, 3, 5} and the next available prime is 7.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A053669-A053674, A191112.

A190911 := proc(n) local k: for k from 3 by 2 do if(gcd(k,n)=1 and gcd(k,n+3)=1)then return k: fi: od: end: seq(A190911(n),n=1..100); # Nathaniel Johnston, May 26 2011

a(15) corrected by Nathaniel Johnston, May 26 2011

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

Original entry on oeis.org

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

Labos Elemer, Nov 26 2003

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

Cf. A090092, A090093.

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}]

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

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

Offset corrected by Mohammed Yaseen, Aug 15 2023

cp's OEIS Frontend

A190911 Least number coprime to n and n+3.

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