A071808 Smallest number s such that s*k+1 is squarefree for 1 <= k <= n.

1, 1, 2, 10, 10, 10, 10, 18, 18, 18, 18, 18, 18, 18, 18, 126, 126, 126, 126, 126, 126, 126, 126, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 270, 1470, 1470, 1470, 1890, 1890, 1890, 2310, 2310, 2310, 2310

Offset

1,3

Comments

a(n)+1 or a(n)-1 is prime for listed terms.

From Amiram Eldar, Apr 30 2025: (Start)

a(76) = 7770, and both 7769 and 7771 are composite. Other terms without a prime neighbor are 307230, 2192190, 3393390, 310390080, 1338557220, and 33910116240.

a(n) is even for n >= 3. (End)

a(n) is divisible by each prime <= sqrt(n). - David A. Corneth, Apr 30 2025

Links

David A. Corneth, Table of n, a(n) for n = 1..1518 (first 762 terms from Amiram Eldar, terms <= 10^18)

David A. Corneth, PARI program

Formula

From Amiram Eldar, Apr 30 2025: (Start)

a(n) >= a(n-1) for n >= 2.

a(n) = A383544(m), for n = A383545(m-1)+1..A383545(m), m >= 2. (End)

Mathematica

a[n_] := a[n] = If[n < 3, 1, Module[{s = 2, m = n + 1}, While[! AllTrue[s*Range[n] + 1, SquareFreeQ], s += 2]; While[SquareFreeQ[s*m + 1], a[m] = s; m++]; s]]; Array[a, 100] (* Amiram Eldar, Apr 30 2025 *)

Prog

(PARI) a(n) = my(s=1); while(sum(i=1, n, issquarefree(s*i+1))<n, s++); s;
(PARI) \\ See Corneth link

Crossrefs

Cf. A005117, A383543, A383544, A383545.

Sequence in context: A215463 A066556 A156556 * A355486 A168381 A212621

Adjacent sequences: A071805 A071806 A071807 * A071809 A071810 A071811

Keyword

nonn

Author

Benoit Cloitre, Jun 06 2002

Status

approved