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 A247485 #10 Feb 16 2025 08:33:23 %S A247485 3,4,5,6,7,8,9,9,10,11,12,13,13,14,14,15,16,16,17,17,18,18,19,19,20, %T A247485 21,21,21,21,22,23,23,24,24,25,25,26,26,26,27,27,27,28,28,29,29,30,30, %U A247485 31,31,31,31,32,32,33,33,33,33,34,34,34,35,36,36,36,36,37 %N A247485 Integer part of 2*sqrt(prime(n)) + 1. %C A247485 A117767(n) = 2*floor(sqrt(prime(n))) + 1 <= a(n); %C A247485 a(A247514(n)) = A117767(A247514(n)); a(A247515(n)) > A117767(A247515(n)). %C A247485 Andrica's conjecture: a(n) <= A001223(n). %H A247485 Reinhard Zumkeller, <a href="/A247485/b247485.txt">Table of n, a(n) for n = 1..10000</a> %H A247485 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AndricasConjecture.html">Andrica's Conjecture</a> %H A247485 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LegendresConjecture.html">Legendre's Conjecture</a> %H A247485 Wikipedia, <a href="http://en.wikipedia.org/wiki/Andrica's_conjecture">Andrica's conjecture</a> %t A247485 Floor[2Sqrt[Prime[Range[70]]]+1] (* _Harvey P. Dale_, Sep 04 2020 *) %o A247485 (Haskell) %o A247485 a247485 = (+ 1) . floor . (* 2) . sqrt . fromIntegral . a000040 %o A247485 (PARI) a(n) = 1+sqrtint(4*prime(n)); \\ _Michel Marcus_, Aug 26 2021 %Y A247485 Cf. A117767, A001223, A000040, A000006, A247514, A247515. %K A247485 nonn %O A247485 1,1 %A A247485 _Reinhard Zumkeller_, Sep 20 2014