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

11411, 111181111, 111111011111, 111111111111112811111111111111

Offset: 1

Author

Altug Alkan, Sep 21 2015

Keywords

• nonn
• base

Comments

Inspiration was symmetry and visual simplicity.

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.

a(5) > 10^6000.

Additionally, same visual inspirations can trigger the ideas of similar sequences.

For example, 1111111111111111111111441111111111111111111111 is a semiprime.

a(5) = (n=4847) = "1" x 4847 . 9694 . "1" x 4847. - Dana Jacobsen, Oct 13 2015

a(6) has n > 6000. - Dana Jacobsen, Oct 13 2015

a(6) has n > 10000 if it exists. - Chai Wah Wu, Oct 22 2015

Examples

			a(1) = 11411 because the concatenation of 11, 4 and 11 is a prime number.
a(2) = 111181111 because the concatenation of 1111, 8 and 1111 is a prime number.
a(3) = 111111011111 because the concatenation of 11111, 10 and 11111 is a prime number.
		

Crossrefs

Cf. A002275, A068817, A070220, A070746, A261364.

Programs

Mathematica

Select[Table[w = Table[1, {k}]; FromDigits@ Join[w, IntegerDigits[2 k], w], {k, 60}], PrimeQ] (* Michael De Vlieger, Sep 21 2015 *)
Select[Table[FromDigits[Flatten[Join[{PadRight[{},n,1],IntegerDigits[2n],PadRight[{},n,1]}]]],{n,20}],PrimeQ] (* Harvey P. Dale, Feb 25 2024 *)

PARI

for(n=1, 1e3, if(isprime(k=eval(Str((10^n - 1)/9, 2*n, (10^n - 1)/9))), print1(k", ")))

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