A065861 Remainder when the n-th composite number is divided by pi(n), the number of primes not exceeding n.

0, 0, 1, 1, 0, 2, 3, 0, 2, 0, 1, 4, 0, 1, 2, 6, 0, 6, 0, 1, 2, 8, 0, 2, 3, 4, 6, 4, 5, 2, 4, 5, 6, 7, 8, 6, 7, 8, 9, 6, 8, 6, 7, 8, 9, 6, 8, 9, 10, 12, 14, 11, 12, 13, 14, 0, 1, 14, 16, 13, 14, 15, 16, 0, 1, 16, 17, 18, 0, 16, 18, 15, 16, 18, 20, 0, 1, 20, 0, 1, 2, 22, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4

Offset

2,6

Links

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

Formula

a(n) = A002808(n) mod A000720(n).

Example

n=100, c(100)=133, pi(100)=25, a(100)=8 because 133 = 5*25 + 8.

Prog

(PARI) Composite(n) = { local(k); k=n + primepi(n) + 1; while (k != n + primepi(k) + 1, k = n + primepi(k) + 1); return(k) } { for (n = 2, 1000, a=Composite(n)%primepi(n); write("b065861.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 02 2009

Crossrefs

Cf. A002808, A000720, A065855-A065864.

Sequence in context: A059067 A356707 A352938 * A329393 A336207 A344909

Adjacent sequences: A065858 A065859 A065860 * A065862 A065863 A065864

Keyword

nonn

Author

Labos Elemer, Nov 26 2001

Status

approved