A079047 Number of primes between prime(n) and prime(n)^2.

1, 2, 6, 11, 25, 33, 54, 64, 90, 136, 151, 207, 250, 269, 314, 393, 470, 501, 590, 655, 684, 789, 863, 976, 1138, 1226, 1267, 1353, 1394, 1493, 1846, 1944, 2108, 2156, 2454, 2511, 2692, 2877, 3004, 3201, 3395, 3470, 3825, 3901, 4044, 4118, 4580, 5058, 5225

Offset: 1

Author

Jose R. Brox (tautocrona(AT)terra.es), Feb 01 2003

Keywords

• nonn

Comments

I conjecture that 25 and 64 are the only terms that are also square numbers.

The next squares are 564001 and 774400, which occur at positions 419 and 481. There are no other squares in the first 10000 terms. - T. D. Noe, Sep 11 2013

Examples

			a(1)=1 because between prime(1)=2 and 2^2=4 there's one prime (3). a(3)=6 because between prime(3)=5 and 5^2=25 there are 6 primes (7, 11, 13, 17, 19, 23).
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055399, A066680.

Cf. A050216.

Programs

Magma

[#PrimesInInterval(NthPrime(n), NthPrime(n)^2)-1: n in [1..70]]; // Vincenzo Librandi, Jul 23 2019

Mathematica

Table[p = Prime[n]; PrimePi[p^2] - n, {n, 100}] (* T. D. Noe, Sep 11 2013 *)

PARI

forprime(p=2,500,res=0; forprime(q=p+1,p^2,res=res+1); print1(res","))

Extensions

Data corrected by T. D. Noe, Oct 25 2006

Edited (removing comment & correction about irrelevant property) by Peter Munn, Jan 24 2023