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Number of primes p such that n^2 < p < n^2 + pi(n), where pi(n) is the number of primes less than n.
1

%I #7 Mar 30 2012 17:22:25

%S 0,0,0,1,0,1,0,1,1,2,0,0,1,2,2,1,1,0,1,1,1,2,0,1,1,2,1,1,0,1,2,2,3,1,

%T 2,3,1,3,2,3,1,0,1,1,2,1,2,2,1,1,1,3,1,2,1,1,4,2,1,2,2,3,0,2,3,3,2,2,

%U 0,2,2,2,2,3,2,3,1,3,2,1,5,2,3,2,4,2,5,3,3,4,4,1,2,3,3,3,5,3,3

%N Number of primes p such that n^2 < p < n^2 + pi(n), where pi(n) is the number of primes less than n.

%C A more restrictive version of the conjecture that there is always a prime between n^2 and (n+1)^2.

%H T. D. Noe, <a href="/A069160/b069160.txt">Table of n, a(n) for n=1..10000</a>

%e a(10)= 2 because pi(10) = 4 and there are 2 primes between 100 and 104.

%t maxN=100; lst={}; For[i=1, i<maxN, i++, n=i^2; cnt=0; k=1; While[k<PrimePi[i], If[PrimeQ[n+k], cnt++ ]; k++ ]; AppendTo[lst, cnt]]; lst

%Y Cf. A000720, A014085.

%K easy,nonn

%O 1,10

%A _T. D. Noe_, Apr 09 2002