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

2,4

Links

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

Formula

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

Example

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]

Mathematica

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

Prog

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

Crossrefs

Cf. A000720, A000040, A065134, A004648.

Sequence in context: A048804 A158565 A132422 * A343033 A307239 A204087

Adjacent sequences: A065130 A065131 A065132 * A065134 A065135 A065136

Keyword

nonn

Author

Labos Elemer, Oct 15 2001

Status

approved