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 A285269 #27 Nov 22 2024 08:38:28
%S A285269 0,3,3,4,4,5,5,6,6,9,7,8,7,9,10,10,9,12,10,11,13,11,14,13,14,13,14,16,
%T A285269 16,15,15,16,17,18,19,14,22,19,18,16,22,18,24,20,22,22,20,23,24,22,23,
%U A285269 21,25,27,24,27,26,25,27,25,23,33,28,25,29,28,31,30,33,29
%N A285269 Number of (odd) primes between 2*n^2 and 2*(n+1)^2.
%C A285269 Essentially the same as A285786, except for the offset and initial values.
%H A285269 Paolo Xausa, <a href="/A285269/b285269.txt">Table of n, a(n) for n = 0..10000</a>
%F A285269 a(n) = A285786(n+1), for all n >= 2.
%F A285269 First differences of A278114, a(n) = A278114(n+1) - A278114(n), for n > 0.
%e A285269 a(0) = 0 because between 2*0^2 = 0 and 2*1^2 = 2, there are no (odd) primes.
%e A285269 a(1) = 3 because between 2*1^2 = 2 and 2*2^2 = 8, there are the 3 (odd) primes 3, 5 and 7.
%e A285269 a(2) = 3 because between 2*2^2 = 8 and 2*3^2 = 18, there are the 3 primes 11, 13 and 17.
%t A285269 Join[{0}, Differences[PrimePi[2*Range[100]^2]]] (* _Paolo Xausa_, Nov 22 2024 *)
%o A285269 (PARI) a(n)=primepi(2*(n+1)^2-1)-primepi(2*n^2)
%K A285269 nonn
%O A285269 0,2
%A A285269 _M. F. Hasler_, May 02 2017