A065863 Remainder when n-th prime is divided by the number of nonprimes not exceeding n.

0, 0, 0, 1, 1, 1, 2, 3, 3, 5, 1, 2, 6, 3, 2, 3, 9, 6, 1, 11, 8, 9, 13, 14, 1, 16, 13, 12, 14, 13, 7, 5, 5, 1, 5, 1, 7, 7, 5, 5, 11, 7, 17, 13, 11, 7, 19, 25, 23, 19, 17, 17, 19, 23, 23, 23, 23, 19, 25, 23, 25, 29, 37, 35, 31, 29, 43, 43, 47, 43, 47, 47, 3, 2, 1, 53, 53, 55, 2, 3, 6, 1, 11, 6

Offset: 1

Author

Labos Elemer, Nov 26 2001

Keywords

• nonn

Examples

			For n=25, prime(25)=97, n - pi(n) = 25 - 9 = 16, a(25)=1 because 97 = 6*16 + 1.
		

Links

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

Crossrefs

Cf. A000040, A062298, A065858-A065864, A065134, A004648, A065133, A065134.

Programs

Mathematica

Table[Mod[Prime[n],n-PrimePi[n]],{n,90}] (* Harvey P. Dale, Aug 04 2015 *)

PARI

a(n) = { prime(n)%(n - primepi(n)) } \\ Harry J. Smith, Nov 02 2009

Formula

a(n) = prime(n) mod (n - pi(n)) = A000040(n) mod A062298(n).