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%I #15 Jul 06 2020 10:04:55
%S 2,2,3,2,2,2,1,2,1,2,2,2,1,2,2,2,2,2,2,2,1,1,1,2,1,2,2,2,2,2,2,2,1,1,
%T 2,2,3,3,2,3,3,3,2,2,1,2,2,2,1,1,2,2,3,3,2,2,2,3,3,3,2,3,3,3,3,3,3,3,
%U 3,3,3,4,3,3,2,2,2,3,3,3,2,2,2,2,2,2,2
%N Number of primes in Breusch's interval [n; 9(n+3)/8].
%C Germán Andrés Paz proves that a(n) > 0 for all nonnegative n. - _Charles R Greathouse IV_, Jul 06 2020
%H Jens Kruse Andersen, <a href="/A248371/b248371.txt">Table of n, a(n) for n = 0..10000</a>
%H Germán Andrés Paz, <a href="http://emis.impa.br/EMIS/journals/GMN/yahoo_site_admin/assets/docs/1_GMN-2642-V15N1.120120222.pdf"> On the Interval [n; 2n]: Primes, Composites and Perfect Powers</a> , Gen. Math. Notes 15 no. 1 (2013), 1-15.
%e a(0)=a(1)=2 because in [0; 9(0+3)/8] = [0; 27/8] and in [1; 9(1+3)/8] = [1; 9/2] there are the two primes 2 and 3.
%e a(2)=3 because in [2; 9(2+3)/8] = [2; 45/8] there are the three primes 2, 3 and 5.
%p with(numtheory): A248371:=n->pi(floor((n+3)*9/8))-pi(n-1): seq(A248371(n), n=0..100); # _Wesley Ivan Hurt_, Oct 05 2014
%t Table[PrimePi[(n + 3)*9/8] - PrimePi[n - 1], {n, 0, 100}] (* _Wesley Ivan Hurt_, Oct 05 2014 *)
%o (PARI) a(n)=primepi((n+3)*9\8)-primepi(n-1)
%K nonn
%O 0,1
%A _M. F. Hasler_, Oct 05 2014
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