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%I #13 May 15 2022 11:48:11
%S 2,5,11,47,163,89,463,479,199,107,241,151,709,151,599,313,547,211,613,
%T 859,863,241,1217,1091,827,311,967,1327,691,1109,1123,829,389,821,857,
%U 431,1301,433,1451,1933,3449,5701,1753,4663,563,3557,4253,1867,4447
%N Prime number of primes between squares of consecutive primes; or, primes occurring in A050216.
%C For small values of n, these numbers exhibit higher and lower values as n increases. Conjecture: There exists an n such that seq(n1) is < seq(n1+1) for all n1 >= n.
%H Harvey P. Dale, <a href="/A089609/b089609.txt">Table of n, a(n) for n = 0..1000</a>
%t Select[PrimePi[#[[2]]]-PrimePi[#[[1]]]&/@Partition[Prime[Range[500]]^2,2,1],PrimeQ] (* _Harvey P. Dale_, May 15 2022 *)
%o (PARI) \ prime number of primes between squares. pbetweensq(n) = { for(x=1,n, c=0; for(y=prime(x)^2, prime((x+1))^2, if(isprime(y),c++) ); if(isprime(c),print1(c",")) ) }
%Y Cf. A000879, A050216.
%K easy,nonn
%O 0,1
%A _Cino Hilliard_, Dec 30 2003
%E Edited by _Ray Chandler_, Jan 05 2004