A217607 Smallest k > 1 such that n divides binomial(n,k).

2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2

Offset

3,1

Links

Antti Karttunen, Table of n, a(n) for n = 3..65539

Formula

From Robert G. Wilson v, Jun 24 2025: (Start)

a(n) = 2 iff n (mod 2) = 1;

a(n) = 3 iff n (mod 6) = {2, 4};

a(n) = 4 iff n (mod 24) = 18;

a(n) = 6 iff n (mod 360) = 300; etc. (End)

Example

a(6) = 5 because 6 divides binomial(6,5) = 6 and 6 does not divide binomial(6,k) for 1 < k < 5.

Maple

with(numtheory):for n from 3 to 100 do:ii:=0: for k from 2 to n while(ii=0) do:z:=binomial(n, k):if irem(z, n)=0 then ii:=1:printf(`%d, `, k):else fi:od:od:

Mathematica

a[n_] := Block[{k = 2}, While[ Mod[ Binomial[n, k], n] > 0, k++]; k]; Array[a, 87, 3] (* Robert G. Wilson v, Jun 24 2025 *)

Prog

(PARI) A217607(n) = for(k=2, oo, if(!(binomial(n, k)%n), return(k))); \\ Antti Karttunen, May 24 2021

Crossrefs

Sequence in context: A112763 A093476 A262597 * A066727 A076606 A056927

Adjacent sequences: A217604 A217605 A217606 * A217608 A217609 A217610

Keyword

nonn

Author

Michel Lagneau, Oct 08 2012

Status

approved