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A211401
a(n) = n-th prime of the form (k concatenated with k concatenated...) n times concatenated with 1.
1
11, 661, 4441, 404040401, 29292929291, 5353535353531, 1291291291291291291291, 81818181818181811, 8888888888888888881, 2532532532532532532532532532531, 2282282282282282282282282282282281, 1201201201201201201201201201201201201, 3813813813813813813813813813813813813811
OFFSET
1,1
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.
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Jonathan Vos Post, Feb 09 2013
STATUS
approved