cp's OEIS Frontend

A262399 Primes that are the concatenation of n 1's, 2*n and n 1's.

%I A262399 #40 Feb 25 2024 11:55:26
%S A262399 11411,111181111,111111011111,111111111111112811111111111111
%N A262399 Primes that are the concatenation of n 1's, 2*n and n 1's.
%C A262399 Inspiration was symmetry and visual simplicity.
%C A262399 Generally, the number of 1's is in the center of the 1's. On the other hand, in a(3) the number of 1's is 11. a(3) has an exceptional property because 2*n contains a digit 1 next to the leading string of 1's; this situation also brings about different a perception in terms of symmetry.
%C A262399 a(5) > 10^6000.
%C A262399 Additionally, same visual inspirations can trigger the ideas of similar sequences.
%C A262399 For example, 1111111111111111111111441111111111111111111111 is a semiprime.
%C A262399 a(5) = (n=4847) = "1" x 4847 . 9694 . "1" x 4847. - _Dana Jacobsen_, Oct 13 2015
%C A262399 a(6) has n > 6000. - _Dana Jacobsen_, Oct 13 2015
%C A262399 a(6) has n > 10000 if it exists. - _Chai Wah Wu_, Oct 22 2015
%e A262399 a(1) = 11411 because the concatenation of 11, 4 and 11 is a prime number.
%e A262399 a(2) = 111181111 because the concatenation of 1111, 8 and 1111 is a prime number.
%e A262399 a(3) = 111111011111 because the concatenation of 11111, 10 and 11111 is a prime number.
%t A262399 Select[Table[w = Table[1, {k}]; FromDigits@ Join[w, IntegerDigits[2 k], w], {k, 60}], PrimeQ] (* _Michael De Vlieger_, Sep 21 2015 *)
%t A262399 Select[Table[FromDigits[Flatten[Join[{PadRight[{},n,1],IntegerDigits[2n],PadRight[{},n,1]}]]],{n,20}],PrimeQ] (* _Harvey P. Dale_, Feb 25 2024 *)
%o A262399 (PARI) for(n=1, 1e3, if(isprime(k=eval(Str((10^n - 1)/9, 2*n, (10^n - 1)/9))), print1(k", ")))
%o A262399 (Perl) use ntheory ":all"; for my $n (1..1e5) { my $s=join("", "1" x $n, 2*$n, "1" x $n); say $s if is_prob_prime($s); } # _Dana Jacobsen_, Oct 13 2015
%Y A262399 Cf. A002275, A068817, A070220, A070746, A261364.
%K A262399 nonn,base
%O A262399 1,1
%A A262399 _Altug Alkan_, Sep 21 2015