A329531 Number of primes between squares of successive even numbers.

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, 26, 28, 24, 29, 29, 29, 32, 30, 30, 30, 36, 32, 35, 36, 41, 33, 39, 33, 43, 36, 40, 42, 42, 43, 44, 45, 41, 42, 43, 47, 51, 49, 47, 52, 40, 57, 53, 52, 52, 48

Offset: 1

Author

Hugo Pfoertner, Nov 15 2019

Keywords

• nonn

Examples

			a(1) = 2: 2 primes (2, 3) between 0 and 4;
a(2) = 4: 4 primes (5, 7, 11, 13) between 4 and 16.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A000720, A014085, A089166.

Programs

Magma

[2] cat [#PrimesInInterval(4*k^2,4*(k+1)^2): k in [1..70]]; // Marius A. Burtea, Nov 17 2019

Maple

2,seq(nops(select(isprime, [seq(j,j=(i-2)^2+1..i^2,2)])),i=4..1000,2); # Robert Israel, Nov 17 2019

PARI

forstep (k=1,129,2,print1(primepi((k+1)^2)-primepi((k-1)^2),", "))

Formula

a(n) = A000720(4*n^2) - A000720(4*(n-1)^2). - Robert Israel, Nov 17 2019