A064722 a(1) = 0; for n >= 2, a(n) = n - (largest prime <= n).

0, 0, 0, 1, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3

Offset: 1

Author

Reinhard Zumkeller, Oct 13 2001

Keywords

• nonn
• easy

Examples

			a(26) = 26 - 23 = 3, a(37) = 37 - 37 = 0.
		

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A000040, A000720, A007917, A007920, A010051, A049711.

Programs

Maple

0, seq(n - prevprime(n+1), n=2..100); # Robert Israel, Aug 25 2014

Mathematica

Join[{0},Table[n-NextPrime[n+1,-1],{n,2,110}]] (* Harvey P. Dale, Aug 23 2011 *)

PARI

{ for (n = 1, 1000, if (n>1, a=n - precprime(n), a=0); write("b064722.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 23 2009

Formula

a(n) = n - A007917(n).

a(n) = 0 iff n is 1 or a prime.

Computable also as a "commutator": pi(prime(m)) - prime(pi(m)) = A000720(A000040(m))-A000040(A000720(m)). Labels position of composites between 2 consecutive primes. - Labos Elemer, Oct 19 2001

a(n) = a(n-1)*0^A010051(n) + 1 - A010051(n), a(1) = 0. - Reinhard Zumkeller, Mar 23 2006

a(n) = n mod A007917(n). - Michel Marcus, Aug 22 2014

a(n) = A049711(n+1) - 1 for n >= 2. - Pontus von Brömssen, Jul 31 2022