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

1,2

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.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Wikipedia, Oppermann's conjecture

Mathematica

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

Prog

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

Crossrefs

Cf. A014085, A089610, A108309, A010051.

Sequence in context: A345971 A211355 A211353 * A122771 A217710 A112190

Adjacent sequences: A094186 A094187 A094188 * A094190 A094191 A094192

Keyword

easy,nonn

Author

Jason Earls, May 25 2004

Status

approved