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

1,1

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A061265, A014085.

Sequence in context: A166744 A080165 A239712 * A307508 A063535 A091653

Adjacent sequences: A224360 A224361 A224362 * A224364 A224365 A224366

Keyword

nonn

Author

César Aguilera, Apr 04 2013

Extensions

Corrected and edited by Giovanni Resta, Apr 10 2013

Status

approved