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

1,1

Links

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

Formula

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

Example

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

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

Prog

(PARI) forstep (k=1, 129, 2, print1(primepi((k+1)^2)-primepi((k-1)^2), ", "))
(Magma) [2] cat [#PrimesInInterval(4*k^2, 4*(k+1)^2): k in [1..70]]; // Marius A. Burtea, Nov 17 2019

Crossrefs

Cf. A000720, A014085, A089166.

Sequence in context: A210936 A140203 A085888 * A187325 A112233 A062249

Adjacent sequences: A329528 A329529 A329530 * A329532 A329533 A329534

Keyword

nonn

Author

Hugo Pfoertner, Nov 15 2019

Status

approved