A094189 Number of primes between n^2-n and n^2 (inclusive).

0, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 2, 2, 2, 3, 4, 4, 3, 4, 3, 3, 4, 5, 4, 3, 4, 5, 4, 4, 5, 4, 4, 5, 5, 2, 6, 6, 5, 4, 6, 4, 5, 7, 7, 3, 7, 8, 4, 5, 10, 7, 5, 6, 5, 5, 10, 7, 8, 8, 6, 10, 7, 5, 5, 8, 7, 7, 5, 10, 7, 8, 10, 7, 7, 10, 10, 9, 12, 7, 11, 10, 10, 9, 7, 13, 11, 10, 10, 11, 10, 11, 10, 11

Offset: 1

Author

Jason Earls, May 25 2004

Keywords

• easy
• nonn

Comments

Conjecture: for n>11, a(n)>1.

Oppermann conjectured in 1882 that a(n)>0 for n>1. - T. D. Noe, Sep 16 2008

References

• Paulo Ribenboim, The New Book of Prime Number Records, 3rd ed., 1995, Springer, p. 248.
• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 183.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Wikipedia, Oppermann's conjecture

Crossrefs

Cf. A014085, A089610, A108309, A010051.

Programs

Haskell

a094189 n = sum $ map a010051' [n*(n-1) .. n^2]
-- Reinhard Zumkeller, Jun 07 2015

Mathematica

Table[PrimePi[n^2]-PrimePi[n^2-n-1],{n,100}] (* Harvey P. Dale, Jul 24 2015 *)

PARI

a(n) = sum(k=n^2-n,n^2,isprime(k))

PARI

a(n)=my(s);forprime(p=n^2-n,n^2,s++);s \\ Charles R Greathouse IV, Jan 18 2016