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a(1) = 3 and then the smallest prime that is obtained by placing digits on both sides of the previous term. Or smallest prime that encompasses a(n-1).
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%I #11 Nov 11 2022 11:51:34

%S 3,131,11311,3113111,231131111,22311311119,3223113111199,

%T 132231131111993,11322311311119931,7113223113111199313,

%U 171132231131111993137,31711322311311119931373,3317113223113111199313733

%N a(1) = 3 and then the smallest prime that is obtained by placing digits on both sides of the previous term. Or smallest prime that encompasses a(n-1).

%t NestList[Select[Flatten[Table[FromDigits[Join[{a},IntegerDigits[#],{b}]],{a,9},{b,1,9,2}]],PrimeQ][[1]]&,3,12] (* _Harvey P. Dale_, Nov 11 2022 *)

%Y Cf. A075595, A075596, A075598, A075599, A075600, A075601, A075602.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Sep 28 2002

%E More terms from _Sascha Kurz_, Jan 20 2003

%E One more term from _David Wasserman_, Jan 20 2005