A224363 Primes p such that there are no squares between p and the prime following p.

2, 5, 11, 17, 19, 29, 37, 41, 43, 53, 59, 67, 71, 73, 83, 89, 101, 103, 107, 109, 127, 131, 137, 149, 151, 157, 163, 173, 179, 181, 191, 197, 199, 211, 227, 229, 233, 239, 241, 257, 263, 269, 271, 277, 281, 293, 307, 311, 313, 331, 337, 347, 349, 353, 367, 373

Offset: 1

Author

César Aguilera, Apr 04 2013

Keywords

• nonn

Comments

Legendre's Conjecture states that there is a prime between n^2 and (n+1)^2 for every integer n > 0 and thus that between two adjacent primes there can be at most one square. As of April 2013, the conjecture is still unproved.

a(n) = A000040(A221056(n)). - Reinhard Zumkeller, Apr 15 2013

Examples

			5 is a term because there are no squares between the adjacent primes 5 and 7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Legendre's Conjecture
• Wikipedia, Legendre's conjecture

Crossrefs

Cf. A061265, A014085.

Programs

Haskell

a224363 = a000040 . a221056  -- Reinhard Zumkeller, Apr 15 2013

Mathematica

Select[Prime[Range[60]], Floor[Sqrt[NextPrime[#]]] == Floor[Sqrt[#]] &] (* Giovanni Resta, Apr 10 2013 *)

Extensions

Corrected and edited by Giovanni Resta, Apr 10 2013