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%I #40 Feb 25 2024 11:55:26
%S 11411,111181111,111111011111,111111111111112811111111111111
%N Primes that are the concatenation of n 1's, 2*n and n 1's.
%C Inspiration was symmetry and visual simplicity.
%C 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 a(5) > 10^6000.
%C Additionally, same visual inspirations can trigger the ideas of similar sequences.
%C For example, 1111111111111111111111441111111111111111111111 is a semiprime.
%C a(5) = (n=4847) = "1" x 4847 . 9694 . "1" x 4847. - _Dana Jacobsen_, Oct 13 2015
%C a(6) has n > 6000. - _Dana Jacobsen_, Oct 13 2015
%C a(6) has n > 10000 if it exists. - _Chai Wah Wu_, Oct 22 2015
%e a(1) = 11411 because the concatenation of 11, 4 and 11 is a prime number.
%e a(2) = 111181111 because the concatenation of 1111, 8 and 1111 is a prime number.
%e a(3) = 111111011111 because the concatenation of 11111, 10 and 11111 is a prime number.
%t Select[Table[w = Table[1, {k}]; FromDigits@ Join[w, IntegerDigits[2 k], w], {k, 60}], PrimeQ] (* _Michael De Vlieger_, Sep 21 2015 *)
%t Select[Table[FromDigits[Flatten[Join[{PadRight[{},n,1],IntegerDigits[2n],PadRight[{},n,1]}]]],{n,20}],PrimeQ] (* _Harvey P. Dale_, Feb 25 2024 *)
%o (PARI) for(n=1, 1e3, if(isprime(k=eval(Str((10^n - 1)/9, 2*n, (10^n - 1)/9))), print1(k", ")))
%o (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 Cf. A002275, A068817, A070220, A070746, A261364.
%K nonn,base
%O 1,1
%A _Altug Alkan_, Sep 21 2015
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