%I A087094
%S A087094 0,9,0,42,22,78,272,342,506,812,465,111,205,903,2162,689,3422,3660,2211,
%T A087094 2485,584,1027,3403,3916,9312,404,3502,5671,11772,12656,5334,17030,1096,
%U A087094 6394,22052,11325,12246,13203,27722,7439,31862,32580,18145,37056,19306
%N A087094 a(n) = smallest k such that (10^k-1)/9 == 0 mod prime(n)^2, or 0 if no 
               such k exists.
%C A087094 For a given a(n)>0, all of the values of k such that (10^k-1)/9=0 mod 
               prime(n)^2 is given by the sequence a(n)*A000027, i.e. integral multiples 
               of a(n). For example, for n=2, prime(2)=3, a(n)=9, the set of values 
               of k for which (10^k-1)/9=0 mod 3^2 is 9*A000027=9,18,27,36,45,...
%C A087094 The union of the collection of sequences formed from the nonzero terms 
               of a(n)*A000027, gives the values of k for which (10^k-1)/9 is not 
               square-free, see A046412. All of terms of the sequence a(n) are integer 
               multiples of prime(n) for primes <1000 except for a(93)=486 where 
               prime(93)=487. Conjecture: there are no 0 terms after a(3).
%e A087094 a(2)=9 since 9 is least value of k for which (10^k-1)/9=0 mod 3^2.
%Y A087094 Cf. A000040, A000042, A046412, A084006, A084007.
%Y A087094 Sequence in context: A076262 A167301 A013534 this_sequence A013535 A167319 
               A057403
%Y A087094 Adjacent sequences: A087091 A087092 A087093 this_sequence A087095 A087096 
               A087097
%K A087094 nonn
%O A087094 1,2
%A A087094 Ray Chandler (rayjchandler(AT)sbcglobal.net), Aug 10 2003