

A262399


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


2




OFFSET

1,1


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


LINKS

Table of n, a(n) for n=1..4.


EXAMPLE

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.


MATHEMATICA

Select[Table[w = Table[1, {k}]; FromDigits@ Join[w, IntegerDigits[2 k], w], {k, 60}], PrimeQ] (* Michael De Vlieger, Sep 21 2015 *)


PROG

(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


CROSSREFS

Cf. A002275, A068817, A070220, A070746, A261364.
Sequence in context: A082440 A083975 A157655 * A115753 A257172 A269217
Adjacent sequences: A262396 A262397 A262398 * A262400 A262401 A262402


KEYWORD

nonn,base


AUTHOR

Altug Alkan, Sep 21 2015


STATUS

approved



