A078763 List primes between (2n-1)^2 and (2n)^2.

2, 3, 11, 13, 29, 31, 53, 59, 61, 83, 89, 97, 127, 131, 137, 139, 173, 179, 181, 191, 193, 227, 229, 233, 239, 241, 251, 293, 307, 311, 313, 317, 367, 373, 379, 383, 389, 397, 443, 449, 457, 461, 463, 467, 479, 541, 547, 557, 563, 569, 571, 631, 641, 643, 647

Offset: 1

Author

Donald S. McDonald, Jan 09 2003

Keywords

• easy
• nonn
• tabf

Comments

Primes are on adjacent sides of the Ulam square prime-spiral.

Examples

			The 2 primes between 3^2=9 (odd) and 4^2=16 (even) are just a(3)=11 and a(4)=13.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014085, A078764.

Programs

Maple

2,seq(op(select(isprime, [seq(i,i=(2*n-1)^2..(2*n)^2,2)])),n=1..20); # Robert Israel, Oct 28 2020

Mathematica

f[n_] := Select[Range[(2n - 1)^2, (2n)^2], PrimeQ];Flatten@Array[f, 13] (* Ray Chandler, May 03 2007 *)

Extensions

Extended by Ray Chandler, May 03 2007