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

1,2

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

Links

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

Example

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).

Mathematica

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

Prog

(PARI) forprime(p=2, 500, res=0; forprime(q=p+1, p^2, res=res+1); print1(res", "))
(Magma) [#PrimesInInterval(NthPrime(n), NthPrime(n)^2)-1: n in [1..70]]; // Vincenzo Librandi, Jul 23 2019

Crossrefs

Cf. A055399, A066680.

Cf. A050216.

Sequence in context: A084308 A067605 A072986 * A160966 A052326 A079118

Adjacent sequences: A079044 A079045 A079046 * A079048 A079049 A079050

Keyword

nonn

Author

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

Extensions

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

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

Status

approved