%I #44 Oct 02 2015 15:47:53

%S 0,3,3,3,5,8,29,5,8,15,3,21,8,3,21,3,8,18,20,92,110,51,102,6,57,23,5,

%T 114,8,32,41,6,236,6,39,60,110,62,36,17,53,21,161,41,159,57,137,42,83,

%U 114,126,80,30,36,278,107,425,111,68,68,95,29,8,53,426,48

%N Smallest k such that A011557(n)//k//rev is prime, where rev is the string of digits of A011557(n) reversed (retaining any leading zeros) and // denotes concatenation.

%C Is a(n) = 0 for any n > 0? If such an n exists, that n is a term of A000079 (cf. Greathouse, 2010).

%C All terms are congruent to 0 or 2 modulo 3, since if k is congruent to 1 modulo 3, 1000...0//k//00...01 is divisible by 3 and thus not prime.

%C a(n) <= A100026(n-1) with equality when a(n) is a palindrome. - _Michel Marcus_, Sep 11 2015

%H Dana Jacobsen, <a href="/A261450/b261450.txt">Table of n, a(n) for n = 0..500</a>

%H C. R. Greathouse IV, <a href="https://www.physicsforums.com/threads/primes-of-form-10-k-1.392807/#post-2659344">Primes of form 10^k + 1?</a>, Physics Forums (message from Apr 6, 2010).

%e a(1) = 3, because 10001, 10101, and 10201 are composite and 10301 is prime.

%e a(6) = 29, because 29 is the smallest k such that 1000000//k//0000001 is prime. The decimal expansion of that prime is 1000000290000001.

%t Table[k = 0; d = IntegerDigits[10^n]; While[! PrimeQ@ FromDigits@ Join[d, IntegerDigits@ k, Reverse@ d], k++]; k, {n, 0, 65}] (* _Michael De Vlieger_, Aug 26 2015 *)

%o (PARI) a(n) = x=10^n; k=0; while(!ispseudoprime(eval(Str(x, k, concat(Vecrev(Str(x)))))), k++); k

%o (Perl) use ntheory ":all"; for my $n (0..50) { my($t,$c)=(0); $t++ while $c=1 . 0 x $n . $t . 0 x $n . 1, !is_prob_prime($c); say "$n $t"; } # _Dana Jacobsen_, Oct 02 2015

%Y Cf. A000079, A011557, A100026, A100028, A100456, A100458, A100459, A258372.

%K nonn,base

%O 0,2

%A _Felix Fröhlich_, Aug 23 2015