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

0,1

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

Mathematica

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

Prog

(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", ")) ) }

Crossrefs

Cf. A000879, A050216.

Sequence in context: A106887 A236044 A285809 * A362525 A277041 A087185

Adjacent sequences: A089606 A089607 A089608 * A089610 A089611 A089612

Keyword

easy,nonn

Author

Cino Hilliard, Dec 30 2003

Extensions

Edited by Ray Chandler, Jan 05 2004

Status

approved