A210720
Primes formed by concatenating n, n, n, n, and 1 for n = 1, 2, 3,....
Original entry on oeis.org
33331, 99991, 242424241, 404040401, 454545451, 464646461, 494949491, 525252521, 575757571, 737373731, 787878781, 949494941, 1021021021021, 1081081081081, 1091091091091, 1211211211211, 1291291291291, 1481481481481, 1511511511511
Offset: 1
a(1) = 33331 because Concat(3,3,3,1) = 3331 which is in A000040.
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[nnnn1: n in [1..200] | IsPrime(nnnn1) where nnnn1 is Seqint([1] cat Intseq(n) cat Intseq(n) cat Intseq(n) cat Intseq(n))]; // Vincenzo Librandi, Mar 15 2013
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A210720 := proc(n)
local p;
[n,n,n,n,1] ;
p := digcatL(%) ;
if isprime(p) then
printf("%d,",p) ;
end if;
end proc:
for n from 1 to 400 do
A210720(n) ;
end do: # R. J. Mathar, Feb 10 2013
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Select[Table[FromDigits[Flatten[{IntegerDigits[n], IntegerDigits[n], IntegerDigits[n], IntegerDigits[n], IntegerDigits[1], {}}]], {n, 200}], PrimeQ] (* Vincenzo Librandi, Mar 15 2013 *)
Select[Table[FromDigits[Join[Flatten[IntegerDigits/@PadRight[{},4,n]],{1}]],{n,200}],PrimeQ] (* Harvey P. Dale, Oct 16 2017 *)
A211401
a(n) = n-th prime of the form (k concatenated with k concatenated...) n times concatenated with 1.
Original entry on oeis.org
11, 661, 4441, 404040401, 29292929291, 5353535353531, 1291291291291291291291, 81818181818181811, 8888888888888888881, 2532532532532532532532532532531, 2282282282282282282282282282282281, 1201201201201201201201201201201201201, 3813813813813813813813813813813813813811
Offset: 1
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.
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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
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Table[Select[Table[10 FromDigits[Flatten[IntegerDigits/@PadRight[{},k,n]]]+1,{n,1000}],PrimeQ][[k]],{k,15}] (* Harvey P. Dale, Oct 13 2022 *)
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