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

Author

Labos Elemer, Nov 26 2001

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A002808, A000720, A065855-A065864.

Programs

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

Formula

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