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a(n) = denominator of fraction a/b, where gcd(a, b) = 1, whose decimal representation has the form (n).(n)(n)(n)... with period (n).
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%I #5 Apr 28 2019 18:36:54

%S 9,9,3,9,9,3,9,9,1,99,9,33,99,99,33,99,99,11,99,99,33,9,99,33,99,99,11

%N a(n) = denominator of fraction a/b, where gcd(a, b) = 1, whose decimal representation has the form (n).(n)(n)(n)... with period (n).

%C Numerators in A172503.

%C Apparently the same as A172502. - _R. J. Mathar_, Feb 21 2010

%e a(10) = 99; 1000/99 = 10.10101010... (period 10).

%e a(9) = 1; 10/1 = 9.9999999...

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Feb 05 2010