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%I #22 Dec 01 2020 03:28:25
%S 3,5,7,29,23,53,89,223,113,331,631,211,1381,1129,1637,4759,2579,3433,
%T 4297,1327,2179,2503,7993,5623,9587,17257,15859,14107,19609,34981,
%U 36433,33247,24281,35617,43331,19661,134513,31397,137029
%N Prime islands: for n >= 2, a(n) = least prime whose adjacent primes are exactly 2n apart; a(1) = 3 by convention.
%C For n > 1: (n) = A000040(A261525(n)+1) for n > 1. - _Reinhard Zumkeller_, Aug 23 2015
%H T. D. Noe, <a href="/A046931/b046931.txt">Table of n, a(n) for n=1..100</a>
%H Abhimanyu Kumar and Anuraag Saxena, <a href="https://arxiv.org/abs/2011.14210">Insulated primes</a>, arXiv:2011.14210 [math.NT], 2020. Mentions this sequence.
%e 29 is in a sea of 6 composites, namely 24, 25, 26, 27, 28 and 30 and is the smallest such number, so a(4) = 29.
%t Join[{3},Transpose[Flatten[Table[Select[Partition[Prime[Range[ 20000]],3,1], Last[#]-First[#]==2 n&,1],{n,2,45}],1]][[2]]] (* _Harvey P. Dale_, May 22 2012 *)
%Y Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.
%Y Another version: see A098968 and A098969.
%Y Cf. A031131. - _Zak Seidov_, Jan 25 2015
%Y Cf. A261525, A000040.
%K nonn,nice
%O 1,1
%A _Marc LeBrun_ and _David W. Wilson_
%E Typo in example fixed by _Zak Seidov_, Jan 25 2015
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