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a(1) = 1; a(2) = 1; a(n) = prime(a(n-1)) + prime(a(n-2)) if n > 2.
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%I #13 Sep 19 2019 02:18:35

%S 1,1,4,9,30,136,882,7626,84448,1159912,19226112,376464500,8556370952,

%T 222510227460,6542050923204,215278202878118,7860760142260830,

%U 316135809596510856

%N a(1) = 1; a(2) = 1; a(n) = prime(a(n-1)) + prime(a(n-2)) if n > 2.

%e a(3) = prime(a(2)) + prime(a(1)) = 2 + 2 = 4.

%t f[x_] := Prime[f[x-1]]+Prime[f[x-2]] {f[1]=1, f[2]=1}; Table[f[w], {w, 1, 15}]

%t nxt[{a_,b_}]:={b,Prime[a]+Prime[b]}; Join[{1},Union[Flatten[NestList[nxt,{1,1},13]]]] (* _Harvey P. Dale_, Sep 17 2013 *)

%K nonn,more

%O 1,3

%A _Joseph L. Pe_, Apr 06 2002

%E More terms from _Labos Elemer_, Apr 11 2003

%E a(16)-a(18) from _Chai Wah Wu_, Sep 18 2019