A065133 Remainder when n-th prime is divided by the number of primes not exceeding n.

0, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 5, 1, 5, 5, 3, 5, 3, 7, 1, 7, 2, 8, 7, 2, 4, 8, 9, 3, 6, 10, 5, 7, 6, 8, 1, 7, 11, 5, 10, 12, 9, 11, 1, 3, 1, 13, 2, 4, 8, 14, 1, 11, 1, 7, 13, 15, 5, 9, 13, 5, 1, 5, 7, 11, 8, 14, 5, 7, 13, 19, 10, 16, 1, 5, 11, 19, 5, 13, 1, 3, 17, 19, 2, 6, 12, 20, 5, 7, 11, 23

Offset: 2

Author

Labos Elemer, Oct 15 2001

Keywords

• nonn

Examples

			n = 2: pi(2) = 1, prime(2) = 3, 3 mod 1 = 0, the first term = a(2);
n = 100: pi(100) = 25, prime(100) = 541, 541 mod 25 = 16 = a(100). [corrected by _Jon E. Schoenfield_, Jun 18 2018]
		

Links

• Harry J. Smith, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A000720, A000040, A065134, A004648.

Programs

Mathematica

Table[Mod[Prime[n],PrimePi[n]],{n,2,100}] (* Harvey P. Dale, Nov 28 2013 *)

PARI

{ for (n=2, 1000, write("b065133.txt", n, " ", prime(n)%primepi(n)) ) } \\ Harry J. Smith, Oct 11 2009

Formula

a(n) = prime(n) mod pi(n) = A000040(n) mod A000720(n), n > 1.