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%I #31 Jan 20 2017 20:00:26
%S 3,5,4,6,2,5,2,4,5,1,5,3,1,2,4,4,1,3,2,1,3,2,3,4,2,0,1,0,1,6,1,2,0,4,
%T 0,2,2,1,2,2,0,3,0,1,0,4,4,1,0,1,1,0,3,1,1,1,0,1,1,0,2,4,1,0,1,3,1,2,
%U 0,1,1,2,1,1,1,1,2,1,1,2,0,2,0,1,0,1,1
%N a(n) = floor(10*(sqrt(prime(n+1)) - sqrt(prime(n)))).
%C If Andrica's conjecture is true, a(n) is at most 1 when n gets very large.
%H Arkadiusz Wesolowski, <a href="/A200324/b200324.txt">Table of n, a(n) for n = 1..10000</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_008.htm">Conjecture 8</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AndricasConjecture.html">Andrica's Conjecture</a>
%H Marek Wolf, <a href="http://arxiv.org/abs/1010.3945">A Note on the Andrica Conjecture</a>, arXiv:1010.3945 [math.NT], 2010.
%F a(n) = floor(10*(sqrt(A000040(n+1)) - sqrt(A000040(n)))).
%e a(9) = 5 because 10*(sqrt(29) - sqrt(23)) = 5.8933328382....
%p A200324:=n->floor(10*(sqrt(ithprime(n+1))-sqrt(ithprime(n)))): seq(A200324(n), n=1..200); # _Wesley Ivan Hurt_, Jan 19 2017
%t Table[Floor[10*(Sqrt[Prime[n + 1]] - Sqrt[Prime[n]])], {n, 100}]
%t Floor[10(Sqrt[Last[#]]-Sqrt[First[#]])]&/@Partition[Prime[Range[90]],2,1] (* _Harvey P. Dale_, Aug 24 2012 *)
%Y Cf. A000040, A079063, A200474.
%K nonn,easy
%O 1,1
%A _Arkadiusz Wesolowski_, Nov 18 2011
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