A089609 Prime number of primes between squares of consecutive primes; or, primes occurring in A050216.

2, 5, 11, 47, 163, 89, 463, 479, 199, 107, 241, 151, 709, 151, 599, 313, 547, 211, 613, 859, 863, 241, 1217, 1091, 827, 311, 967, 1327, 691, 1109, 1123, 829, 389, 821, 857, 431, 1301, 433, 1451, 1933, 3449, 5701, 1753, 4663, 563, 3557, 4253, 1867, 4447

Offset: 0

Author

Cino Hilliard, Dec 30 2003

Keywords

• easy
• nonn

Comments

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.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000879, A050216.

Programs

Mathematica

Select[PrimePi[#[[2]]]-PrimePi[#[[1]]]&/@Partition[Prime[Range[500]]^2,2,1],PrimeQ] (* Harvey P. Dale, May 15 2022 *)

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",")) ) }

Extensions

Edited by Ray Chandler, Jan 05 2004