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A329531 Number of primes between squares of successive even numbers.

%I A329531 #17 Sep 08 2022 08:46:24
%S A329531 2,4,5,7,7,9,10,10,12,12,14,13,17,15,17,18,19,19,18,23,23,21,24,23,25,
%T A329531 26,28,24,29,29,29,32,30,30,30,36,32,35,36,41,33,39,33,43,36,40,42,42,
%U A329531 43,44,45,41,42,43,47,51,49,47,52,40,57,53,52,52,48
%N A329531 Number of primes between squares of successive even numbers.
%H A329531 Robert Israel, <a href="/A329531/b329531.txt">Table of n, a(n) for n = 1..2500</a>
%F A329531 a(n) = A000720(4*n^2) - A000720(4*(n-1)^2). - _Robert Israel_, Nov 17 2019
%e A329531 a(1) = 2: 2 primes (2, 3) between 0 and 4;
%e A329531 a(2) = 4: 4 primes (5, 7, 11, 13) between 4 and 16.
%p A329531 2,seq(nops(select(isprime, [seq(j,j=(i-2)^2+1..i^2,2)])),i=4..1000,2); # _Robert Israel_, Nov 17 2019
%o A329531 (PARI) forstep (k=1,129,2,print1(primepi((k+1)^2)-primepi((k-1)^2),", "))
%o A329531 (Magma) [2] cat [#PrimesInInterval(4*k^2,4*(k+1)^2): k in [1..70]]; // _Marius A. Burtea_, Nov 17 2019
%Y A329531 Cf. A000720, A014085, A089166.
%K A329531 nonn
%O A329531 1,1
%A A329531 _Hugo Pfoertner_, Nov 15 2019