login
A094189
Number of primes between n^2-n and n^2 (inclusive).
8
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.
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
KEYWORD
easy,nonn
AUTHOR
Jason Earls, May 25 2004
STATUS
approved