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a(1) = 1; a(n) = prime((a(n-1)+3)/2).
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%I #4 Apr 01 2019 12:55:49

%S 1,3,5,7,11,17,29,53,107,257,733,2503,10211,49739,285377,1909561,

%T 14736529,129812899,1293238351,14448382721,179668662139,2470072307533,

%U 37316454626819

%N a(1) = 1; a(n) = prime((a(n-1)+3)/2).

%t a[1]=1;a[n_]:=a[n]=Prime[(a[n-1]+3)/2];Table[a[n],{n,20}]

%t NestList[Prime[(#+3)/2]&,1,21] (* _Harvey P. Dale_, Apr 01 2019 *)

%Y Cf. A104296, A104298.

%K nonn

%O 1,2

%A _Zak Seidov_, Feb 16 2006

%E More terms from _Harvey P. Dale_, Apr 01 2019