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a(1)=1, a(2)=5, then a(n)=a(n-2)+4, if n odd else a(n)=prime(primepi(a(n-2)+4)).
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%I #2 Mar 30 2012 17:26:35

%S 1,5,5,17,9,31,13,47,17,67,21,83,25,103,29,127,33,149,37,167,41,191,

%T 45,211,49,233,53,257,57,277,61,307,65,331,69,353,73,379,77,401,81,

%U 431,85,449,89,467,93,499,97,523,101,563,105,587,109,607,113,631,117,653,121

%N a(1)=1, a(2)=5, then a(n)=a(n-2)+4, if n odd else a(n)=prime(primepi(a(n-2)+4)).

%t (*1*)Flatten[Table[{k,Prime[k+2]},{k,1,200,4}]]

%t (*2*)s={1};a=1; Do[AppendTo[s,{Prime[a+2],a=a+4}],{100}];Flatten[s]

%K nonn

%O 1,2

%A _Zak Seidov_, Jul 24 2010