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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

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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