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A086517 a(1) = 1 and then the smallest odd number not included earlier such that the arithmetic mean of a pair of successive terms is prime.

%I A086517 #12 Jun 30 2015 14:26:33
%S A086517 1,3,7,15,11,23,35,27,19,39,43,31,51,55,63,59,47,71,75,67,79,87,91,
%T A086517 103,99,95,83,111,107,119,135,127,147,115,139,123,131,143,155,159,167,
%U A086517 179,183,151,163,171,175,187,195,191,203,219,227,231,215,207,239,243,211
%N A086517 a(1) = 1 and then the smallest odd number not included earlier such that the arithmetic mean of a pair of successive terms is prime.
%C A086517 Second term onwards rearrangement of odd numbers of the type 4n+3.
%H A086517 Reinhard Zumkeller, <a href="/A086517/b086517.txt">Table of n, a(n) for n = 1..10000</a>
%o A086517 (PARI) v=[1];n=1;while(n<100,s=(n+v[#v])/2;if(type(s)=="t_INT",if(isprime(s)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0));n++);v \\ _Derek Orr_, Jun 16 2015
%o A086517 (Haskell)
%o A086517 import Data.List (delete)
%o A086517 a086517 n = a086517_list !! (n-1)
%o A086517 a086517_list = 1 : f 1 [3, 5 ..] where
%o A086517    f x zs = g zs where
%o A086517      g (y:ys) = if a010051' ((x + y) `div` 2) == 1
%o A086517                    then y : f y (delete y zs) else g ys
%o A086517 -- _Reinhard Zumkeller_, Jun 30 2015
%Y A086517 Cf. A086518.
%Y A086517 Cf. A259565, A259260, A259429, A259542, A010051, A005408.
%K A086517 nonn
%O A086517 1,2
%A A086517 _Amarnath Murthy_, Jul 30 2003
%E A086517 More terms from _David Wasserman_, Mar 10 2005