A053670 Least number coprime to n and n+1.

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

Offset: 1

Author

Henry Bottomley, Feb 15 2000

Keywords

• nonn
• nice
• easy

Comments

A179675(n) = smallest m such that a(m) = n-th odd prime. - Reinhard Zumkeller, Jul 23 2010

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053669-A053674.

Programs

Haskell

a053670 n = head [x | x <- [3, 5 ..],
                      n `gcd` x == 1, (n + 1) `gcd` x == 1]
-- Reinhard Zumkeller, Dec 28 2012

Mathematica

a[n_] := For[k = 3, True, k++, If[CoprimeQ[k, n, n+1], Return[k]]]; Table[a[n], {n, 1, 101}] (* Jean-François Alcover, Sep 20 2012 *)

PARI

a(n)=my(N=n*(n+1),k=2); while(gcd(k++,N)>1,); k \\ Charles R Greathouse IV, Nov 10 2015

Python

from math import gcd
def a(n):
    k, m = 3, n*(n+1)
    while gcd(k, m) != 1: k += 2
    return k
print([a(n) for n in range(1, 102)]) # Michael S. Branicky, Sep 25 2021

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000 and James Sellers, Feb 22 2000