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%I #9 Aug 26 2021 11:45:22
%S 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 21,21,21,21,22,23,23,24,24,25,25,26,26,26,27,27,27,28,28,29,29,30,30,
%U 31,31,31,31,32,32,33,33,33,33,34,34,34,35,36,36,36,36,37
%N Integer part of 2*sqrt(prime(n)) + 1.
%C A117767(n) = 2*floor(sqrt(prime(n))) + 1 <= a(n);
%C a(A247514(n)) = A117767(A247514(n)); a(A247515(n)) > A117767(A247515(n)).
%C Andrica's conjecture: a(n) <= A001223(n).
%H Reinhard Zumkeller, <a href="/A247485/b247485.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AndricasConjecture.html">Andrica's Conjecture</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LegendresConjecture.html">Legendre's Conjecture</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Andrica's_conjecture">Andrica's conjecture</a>
%t Floor[2Sqrt[Prime[Range[70]]]+1] (* _Harvey P. Dale_, Sep 04 2020 *)
%o (Haskell)
%o a247485 = (+ 1) . floor . (* 2) . sqrt . fromIntegral . a000040
%o (PARI) a(n) = 1+sqrtint(4*prime(n)); \\ _Michel Marcus_, Aug 26 2021
%Y Cf. A117767, A001223, A000040, A000006, A247514, A247515.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Sep 20 2014
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