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%I #6 Dec 17 2019 13:51:02
%S 3,5,23,53,211,211,211,1847,2179,2179,3967,16033,16033,24281,24281,
%T 24281,38501,38501,38501,38501,38501,58831,203713,206699,206699,
%U 413353,413353,413353,1272749,1272749,1272749,1272749,2198981,2198981,2198981
%N Least prime such that the distance to the two adjacent primes is 2n or greater.
%C Erdos and Suranyi call these reclusive primes and prove that such a prime exists for all n. Except for a(0), the record values are in A023186.
%D Paul Erdős and Janos Suranyi, Topics in the theory of numbers, Springer, 2003.
%e a(3)=53 because the adjacent primes 47 and 59 are at distance 6 and all smaller primes have a closer distance.
%t k=2; Table[While[Prime[k]-Prime[k-1]<2n || Prime[k+1]-Prime[k]<2n, k++ ]; Prime[k], {n,0,40}]
%Y Cf. A023186, A087770, A330428.
%K nonn
%O 0,1
%A _T. D. Noe_, Jul 21 2006
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