A339749 a(n) is the greatest k > 0 such that 1+n, 1+2*n, ..., 1+n*k are pairwise coprime.

2, 3, 2, 4, 2, 7, 2, 3, 2, 4, 2, 6, 2, 3, 2, 4, 2, 7, 2, 3, 2, 4, 2, 5, 2, 3, 2, 4, 2, 9, 2, 3, 2, 4, 2, 8, 2, 3, 2, 4, 2, 6, 2, 3, 2, 4, 2, 7, 2, 3, 2, 4, 2, 5, 2, 3, 2, 4, 2, 11, 2, 3, 2, 4, 2, 8, 2, 3, 2, 4, 2, 6, 2, 3, 2, 4, 2, 7, 2, 3, 2, 4, 2, 5, 2, 3, 2

Offset

1,1

Comments

This sequence is well defined: for any n > 0, if p > 1 divides 1+n, then p divides 1+n*(1+p), gcd(1+n, 1+n*(1+p)) > 1 and a(n) <= p.

This sequence is unbounded.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = 2 for any odd n.

a(n!) > n for any n >= 0.

a(n) <= A020639(n+1).

Example

For n = 2:
- gcd(1+2*1, 1+2*2) = 1,
- gcd(1+2*1, 1+2*3) = 1,
- gcd(1+2*2, 1+2*3) = 1,
- however gcd(1+2*1, 1+2*4) = 3,
- so a(2) = 3.

Prog

(PARI) a(n) = { my (p=1); for (k=1, oo, if (gcd(p, 1+n*k)>1, return (k-1), p*=1+n*k)) }

Crossrefs

Cf. A020639, A339743, A339759.

Sequence in context: A155520 A365784 A235912 * A277859 A308566 A288535

Adjacent sequences: A339746 A339747 A339748 * A339750 A339751 A339752

Keyword

nonn

Author

Rémy Sigrist, Dec 16 2020

Status

approved