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A211401 a(n) = n-th prime of the form (k concatenated with k concatenated...) n times concatenated with 1.

%I A211401 #12 Oct 13 2022 14:39:46
%S A211401 11,661,4441,404040401,29292929291,5353535353531,
%T A211401 1291291291291291291291,81818181818181811,8888888888888888881,
%U A211401 2532532532532532532532532532531,2282282282282282282282282282282281,1201201201201201201201201201201201201,3813813813813813813813813813813813813811
%N A211401 a(n) = n-th prime of the form (k concatenated with k concatenated...) n times concatenated with 1.
%C A211401 Main diagonal A[n,n] of array A[k,n] = n-th prime of the form (j concatenated with j concatenated...) k times concatenated with 1.
%e A211401 a(1) = 11 because that is the 1st (smallest) prime of the form Concatenate(1 copy of k) with 1, for k = 1, 2, 3, ....
%e A211401 a(2) = 661 because the 1st (smallest) prime of the form Concatenate(2 copies of k) with 1, for k = 1, 2, 3, .... is 331, and the 2nd is 661.
%e A211401 a(3) = 4441 because the 1st (smallest) prime of the form Concatenate(3 copies of k) with 1, for k = 1, 2, 3, .... is 2221, the 2nd is 3331, and the 3rd is 4441.
%e A211401 a(4) = 404040401 because the 1st (smallest) prime of the form Concatenate(4 copies of k) with 1, for k = 1, 2, 3, .... is 33331, the 2nd is 99991, the 3rd is 242424241, and the 4th is 404040401.
%p A211401 A211401k := proc(n,k)
%p A211401     option remember;
%p A211401     local p,amin;
%p A211401     if n = 1 then
%p A211401         amin := 1 ;
%p A211401     else
%p A211401         amin := procname(n-1,k)+1 ;
%p A211401     end if;
%p A211401     for a from amin do
%p A211401         [seq(a,i=1..k),1] ;
%p A211401         p := digcatL(%) ;
%p A211401         if isprime(p) then
%p A211401             return a;
%p A211401         end if;
%p A211401     end do:
%p A211401 end proc:
%p A211401 A211401 := proc(n)
%p A211401     b := A211401k(n,n) ;
%p A211401     [seq(b,i=1..n),1] ;
%p A211401     digcatL(%) ;
%p A211401 end proc: # _R. J. Mathar_, Feb 10 2013
%t A211401 Table[Select[Table[10 FromDigits[Flatten[IntegerDigits/@PadRight[{},k,n]]]+1,{n,1000}],PrimeQ][[k]],{k,15}] (* _Harvey P. Dale_, Oct 13 2022 *)
%Y A211401 Cf. A030430, A210511, A210712, A210720.
%K A211401 nonn,easy,base
%O A211401 1,1
%A A211401 _Jonathan Vos Post_, Feb 09 2013