A089609 - OEIS

%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