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Remainder when the n-th composite number is divided by pi(n), the number of primes not exceeding n.
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%I #10 Jun 17 2018 01:59:43

%S 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,

%T 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,

%U 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

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

%H Harry J. Smith, <a href="/A065861/b065861.txt">Table of n, a(n) for n = 2..1000</a>

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

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

%o (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

%Y Cf. A002808, A000720, A065855-A065864.

%K nonn

%O 2,6

%A _Labos Elemer_, Nov 26 2001