The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A262399 Primes that are the concatenation of n 1's, 2*n and n 1's. 2
 11411, 111181111, 111111011111, 111111111111112811111111111111 (list; graph; refs; listen; history; text; internal format)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 17 17:32 EDT 2021. Contains 345085 sequences. (Running on oeis4.)