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A224363
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Primes p such that there are no squares between p and the prime following p.
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2
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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
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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5 is a term because there are no squares between the adjacent primes 5 and 7.
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MATHEMATICA
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Select[Prime[Range[60]], Floor[Sqrt[NextPrime[#]]] == Floor[Sqrt[#]] &] (* Giovanni Resta, Apr 10 2013 *)
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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