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%I A224363 #13 Apr 15 2013 10:07:35
%S A224363 2,5,11,17,19,29,37,41,43,53,59,67,71,73,83,89,101,103,107,109,127,
%T A224363 131,137,149,151,157,163,173,179,181,191,197,199,211,227,229,233,239,
%U A224363 241,257,263,269,271,277,281,293,307,311,313,331,337,347,349,353,367,373
%N A224363 Primes p such that there are no squares between p and the prime following p.
%C A224363 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.
%C A224363 a(n) = A000040(A221056(n)). - _Reinhard Zumkeller_, Apr 15 2013
%H A224363 Reinhard Zumkeller, <a href="/A224363/b224363.txt">Table of n, a(n) for n = 1..10000</a>
%H A224363 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LegendresConjecture.html">Legendre's Conjecture</a>
%H A224363 Wikipedia, <a href="http://en.wikipedia.org/wiki/Legendre%27s_conjecture">Legendre's conjecture</a>
%e A224363 5 is a term because there are no squares between the adjacent primes 5 and 7.
%t A224363 Select[Prime[Range[60]], Floor[Sqrt[NextPrime[#]]] == Floor[Sqrt[#]] &] (* _Giovanni Resta_, Apr 10 2013 *)
%o A224363 (Haskell)
%o A224363 a224363 = a000040 . a221056  -- _Reinhard Zumkeller_, Apr 15 2013
%Y A224363 Cf. A061265, A014085.
%K A224363 nonn
%O A224363 1,1
%A A224363 _César Aguilera_, Apr 04 2013
%E A224363 Corrected and edited by _Giovanni Resta_, Apr 10 2013

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