Search: id:A127100
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%I A127100
%S A127100 1,3,9,111,333,3003003,111111111,225121209,675363627
%N A127100 Numbers n such that n^2 divides 10^n-1.
%C A127100 a(n) is a subset of A014950(n) = {1, 3, 9, 27, 81, 111, 243, 333, 729, 
               999, ...} Numbers n such that n divides 10^n-1.
%C A127100 No more terms through 14*10^9. - Ryan Propper (rpropper(AT)stanford.edu), 
               Jan 06 2007
%C A127100 First 7 terms are palindromes. a(n) is divisible by 3 for 1<n<10. 3^2 
               divides a(n) for n = {3,5,6,7,9}. 37 divides a(n) for n = {4,5,7,
               8,9}. Prime factors of a(n) are {3,37,333667,2028119,...}. Note that 
               a(3)/a(2) = a(5)/a(4) = a(9)/a(8) = 3 and a(7)/a(6) = 37. - Alexander 
               Adamchuk (alex(AT)kolmogorov.com), Jan 25 2007
%t A127100 Select[Range[20000], IntegerQ[(PowerMod[10, #, #^2 ]-1)/#^2 ]&]
%Y A127100 Cf. A127101, A127102, A127103, A123104, A127105, A127106, A127107, A127092. 
               Cf. A014950 = numbers n such that n divides 10^n-1.
%Y A127100 Sequence in context: A018746 A053914 A018757 this_sequence A018778 A082606 
               A062702
%Y A127100 Adjacent sequences: A127097 A127098 A127099 this_sequence A127101 A127102 
               A127103
%K A127100 hard,more,nonn
%O A127100 1,2
%A A127100 Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 05 2007, Jan 07 2006
%E A127100 More terms from Ryan Propper (rpropper(AT)stanford.edu), Jan 06 2007

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