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

11, 661, 4441, 404040401, 29292929291, 5353535353531, 1291291291291291291291, 81818181818181811, 8888888888888888881, 2532532532532532532532532532531, 2282282282282282282282282282282281, 1201201201201201201201201201201201201, 3813813813813813813813813813813813813811

Offset: 1

Author

Jonathan Vos Post, Feb 09 2013

Keywords

• nonn
• easy
• base

Comments

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.

Examples

			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, ....
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.
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.
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.
		

Crossrefs

Cf. A030430, A210511, A210712, A210720.

Programs

Maple

A211401k := proc(n,k)
    option remember;
    local p,amin;
    if n = 1 then
        amin := 1 ;
    else
        amin := procname(n-1,k)+1 ;
    end if;
    for a from amin do
        [seq(a,i=1..k),1] ;
        p := digcatL(%) ;
        if isprime(p) then
            return a;
        end if;
    end do:
end proc:
A211401 := proc(n)
    b := A211401k(n,n) ;
    [seq(b,i=1..n),1] ;
    digcatL(%) ;
end proc: # R. J. Mathar, Feb 10 2013

Mathematica

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