A215619 a(n) is the number of consecutive terms of A100071, beginning with index n, which are divisible by n.

4, 1, 6, 1, 8, 1, 4, 1, 12, 5, 14, 1, 4, 1, 18, 1, 20, 1, 4, 1, 24, 1, 6, 1, 4, 1, 30, 21, 32, 1, 12, 1, 8, 1, 38, 1, 14, 1, 42, 1, 44, 1, 6, 1, 48, 1, 8, 1, 4, 1, 54, 1, 6, 9, 4, 1, 60, 1, 62, 1, 4, 1, 6, 1, 68, 1, 4, 1, 72, 1, 74, 1, 4, 1, 12, 1, 80, 1, 4, 1

Offset

3,1

Comments

a(n) = n+1 iff n is prime.

a(n) = 1 iff n in { A067315 }.

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

{ n : a(2n)>1 } = { A058008 } \ { 1 }.

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Maple

b:= proc(n) b(n):= n * binomial(n-1, floor((n-1)/2)) end:
a:= proc(n) local k;
      for k from 0 while irem(b(n+k), n)=0 do od; k
    end:
seq (a(n), n=3..100);  # Alois P. Heinz, Aug 17 2012

Mathematica

b[n_] := n Binomial[n-1, Floor[(n-1)/2]];
a[n_] := Module[{k = 0}, While[Mod[b[n+k], n] == 0, k++]; k];
a /@ Range[3, 100] (* Jean-François Alcover, Nov 22 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A067315, A100071.

Sequence in context: A185093 A010779 A354254 * A136706 A326478 A324118

Adjacent sequences: A215616 A215617 A215618 * A215620 A215621 A215622

Keyword

nonn

Author

Vladimir Shevelev, Aug 17 2012

Status

approved