|
%I #28 Oct 03 2021 09:31:02
%S 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,
%T 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,
%U 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
%N Number of primes between n^2-n and n^2 (inclusive).
%C Conjecture: for n>11, a(n)>1.
%C Oppermann conjectured in 1882 that a(n)>0 for n>1. - _T. D. Noe_, Sep 16 2008
%D Paulo Ribenboim, The New Book of Prime Number Records, 3rd ed., 1995, Springer, p. 248.
%H T. D. Noe, <a href="/A094189/b094189.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Oppermann%27s_conjecture">Oppermann's conjecture</a>
%t Table[PrimePi[n^2]-PrimePi[n^2-n-1],{n,100}] (* _Harvey P. Dale_, Jul 24 2015 *)
%o (PARI) a(n) = sum(k=n^2-n,n^2,isprime(k))
%o (PARI) a(n)=my(s);forprime(p=n^2-n,n^2,s++);s \\ _Charles R Greathouse IV_, Jan 18 2016
%o (Haskell)
%o a094189 n = sum $ map a010051' [n*(n-1) .. n^2]
%o -- _Reinhard Zumkeller_, Jun 07 2015
%Y Cf. A014085, A089610, A108309, A010051.
%K easy,nonn
%O 1,2
%A _Jason Earls_, May 25 2004
|
