This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A089610 #28 Apr 21 2025 11:26:47
%S A089610 1,1,1,2,1,2,1,2,2,4,2,2,3,2,4,4,1,2,3,3,4,4,2,4,4,4,4,4,4,4,5,5,6,4,
%T A089610 5,7,3,6,6,8,5,5,7,4,6,7,6,7,6,6,5,9,7,7,6,7,7,6,8,8,7,7,8,9,11,7,8,
%U A089610 10,8,11,8,7,7,10,11,12,4,9,11,6,9,9,10,8,9,8,11,8,8,9,10,8,13,10,9,10,14,12
%N A089610 Number of primes between n^2 and (n+1/2)^2.
%C A089610 For small values of n, these numbers exhibit higher and lower values as n increases. Conjectures: After n=17 a(n) > 1. There exists an n_1 such that a(n) is < a(n+1) for all n >= n_1.
%C A089610 Same as the number of primes between n^2 and n^2+n. Oppermann conjectured in 1882 that a(n)>0. - _T. D. Noe_, Sep 16 2008
%D A089610 Paulo Ribenboim, The New Book of Prime Number Records, 3rd ed., 1995, Springer, p. 248.
%D A089610 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 183.
%H A089610 T. D. Noe, <a href="/A089610/b089610.txt">Table of n, a(n) for n=1..10000</a>
%H A089610 Wikipedia, <a href="http://en.wikipedia.org/wiki/Oppermann%27s_conjecture">Oppermann's conjecture</a>
%t A089610 a[n_] := PrimePi[(n + 1/2)^2] - PrimePi[n^2]; Table[ a@n, {n, 100}] (* _Robert G. Wilson v_, May 04 2009 *)
%o A089610 (PARI) a(n) = primepi(n^2+n) - primepi(n^2); \\ _Michel Marcus_, May 18 2020
%o A089610 (Haskell)
%o A089610 a089610 n = sum $ map a010051' [n^2 .. n*(n+1)]
%o A089610 -- _Reinhard Zumkeller_, Jun 07 2015
%Y A089610 Cf. A010051, A014085, A094189, A108309.
%K A089610 easy,nonn
%O A089610 1,4
%A A089610 _Cino Hilliard_, Dec 30 2003