cp's OEIS Frontend

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

%I A065133 #13 Jun 18 2018 03:37:53
%S A065133 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,
%T A065133 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,
%U A065133 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
%N A065133 Remainder when n-th prime is divided by the number of primes not exceeding n.
%H A065133 Harry J. Smith, <a href="/A065133/b065133.txt">Table of n, a(n) for n = 2..1000</a>
%F A065133 a(n) = prime(n) mod pi(n) = A000040(n) mod A000720(n), n > 1.
%e A065133 n = 2: pi(2) = 1, prime(2) = 3, 3 mod 1 = 0, the first term = a(2);
%e A065133 n = 100: pi(100) = 25, prime(100) = 541, 541 mod 25 = 16 = a(100). [corrected by _Jon E. Schoenfield_, Jun 18 2018]
%t A065133 Table[Mod[Prime[n],PrimePi[n]],{n,2,100}] (* _Harvey P. Dale_, Nov 28 2013 *)
%o A065133 (PARI) { for (n=2, 1000, write("b065133.txt", n, " ", prime(n)%primepi(n)) ) } \\ _Harry J. Smith_, Oct 11 2009
%Y A065133 Cf. A000720, A000040, A065134, A004648.
%K A065133 nonn
%O A065133 2,4
%A A065133 _Labos Elemer_, Oct 15 2001