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%I #11 Mar 11 2014 20:31:20
%S 7,13,14,21,26,28,35,39,42,52,56,63,65,70,77,78,84,91,104,105,112,117,
%T 126,130,140,143,154,156,168,175,182,189,195,208,210,224,231,234,252,
%U 259,260,273,280,286,297,308,312,315,325,336,350,351,364,378,385,390
%N Integers n for which the period of the decimal expansion of 1/n is 6.
%C The initial terms in the sequence are multiples of either 7 or 13, but the sequence is not exclusively so. a(45) = 297 whose factors include neither 7 nor 13. Next is a(57) = 407 whose factors are 11 and 37.
%e a(1) = 7 because 1/7 = 0.142857142857142857+, whose repeating decimal (142857) is 6 digits long.
%e a(57) = 407 because 1/407 = 0.0024570024570024+, whose repeating decimal (002457) is 6 digits long.
%t Transpose[Select[Table[{n,Length[RealDigits[1/n][[1,-1]]]},{n,500}],#[[2]]==6&]][[1]] (* _Harvey P. Dale_, Dec 04 2010 *)
%K nonn,base
%O 1,1
%A _Gil Broussard_, Aug 15 2006
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