A211401 - OEIS

%I #12 Oct 13 2022 14:39:46

%S 11,661,4441,404040401,29292929291,5353535353531,

%T 1291291291291291291291,81818181818181811,8888888888888888881,

%U 2532532532532532532532532532531,2282282282282282282282282282282281,1201201201201201201201201201201201201,3813813813813813813813813813813813813811

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

%C 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 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 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 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 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 A211401k := proc(n,k)

%p     option remember;

%p     local p,amin;

%p     if n = 1 then

%p         amin := 1 ;

%p     else

%p         amin := procname(n-1,k)+1 ;

%p     end if;

%p     for a from amin do

%p         [seq(a,i=1..k),1] ;

%p         p := digcatL(%) ;

%p         if isprime(p) then

%p             return a;

%p         end if;

%p     end do:

%p end proc:

%p A211401 := proc(n)

%p     b := A211401k(n,n) ;

%p     [seq(b,i=1..n),1] ;

%p     digcatL(%) ;

%p end proc: # _R. J. Mathar_, Feb 10 2013

%t Table[Select[Table[10 FromDigits[Flatten[IntegerDigits/@PadRight[{},k,n]]]+1,{n,1000}],PrimeQ][[k]],{k,15}] (* _Harvey P. Dale_, Oct 13 2022 *)

%Y Cf. A030430, A210511, A210712, A210720.

%K nonn,easy,base

%O 1,1

%A _Jonathan Vos Post_, Feb 09 2013