This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A224363 #14 Feb 16 2025 08:33:19 %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="https://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