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.
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
KEYWORD
nonn
AUTHOR
César Aguilera, Apr 04 2013
EXTENSIONS
Corrected and edited by Giovanni Resta, Apr 10 2013
STATUS
approved