A072681 a(n) = (n - A007917(n)) * (A007918(n) - n).

0, 0, 1, 0, 1, 0, 3, 4, 3, 0, 1, 0, 3, 4, 3, 0, 1, 0, 3, 4, 3, 0, 5, 8, 9, 8, 5, 0, 1, 0, 5, 8, 9, 8, 5, 0, 3, 4, 3, 0, 1, 0, 3, 4, 3, 0, 5, 8, 9, 8, 5, 0, 5, 8, 9, 8, 5, 0, 1, 0, 5, 8, 9, 8, 5, 0, 3, 4, 3, 0, 1, 0, 5, 8, 9, 8, 5, 0, 3, 4, 3, 0, 5, 8, 9, 8, 5, 0, 7, 12, 15, 16, 15, 12, 7, 0, 3, 4, 3, 0, 1, 0

Offset: 2

Author

Reinhard Zumkeller, Jul 01 2002

Keywords

• nonn
• nice
• look

Comments

a(n)=0 iff n is prime.

Local maxima occur at interprimes: a(A024675(n)) = A074927(n+1). - Reinhard Zumkeller, Mar 04 2009

Expanding upon the maxima comment, repetitive subset triplets (like 3,4,3) of form (k,k+1,k) occur when the middle value is a square. - Bill McEachen, Apr 14 2025

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A007917, A007918, A007920, A024675, A064722, A072680, A074927.

Programs

Mathematica

a[n_] := (n - NextPrime[n+1, -1])*(NextPrime[n] - n); Table[a[n], {n, 2, 103}] (* Jean-François Alcover, Jun 14 2013 *)

Formula

a(n) = A064722(n) * A007920(n).

a(n) = A064722(n) * (A072680(n) - A064722(n)).