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Numbers n such that n equals the partial or complete sum of the decimal digits of 1/n, up to the point at which the digits recur or terminate.
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%I #5 Jul 13 2014 10:28:16

%S 3,7,8,13,14,34,43,49,51,76,83,92,94,98,103,109,113,127,139,141,169,

%T 177,179,181,194,218,229,283,323,338,367,394,397,401,437,524,526,537,

%U 579,587,626,659,661,673,674,687,701,719,724,743,767,769,802,823,838

%N Numbers n such that n equals the partial or complete sum of the decimal digits of 1/n, up to the point at which the digits recur or terminate.

%C The digits summed are those before the decimal expansion recurs or terminates. Otherwise reciprocals that supply a recurrent 1, like 1/9 = 0.111... or 1/99 = 0.010101..., would always produce a sum equal to n from sufficient terms of the reciprocal.

%e 1/3 = 0.3... and 3 = 0 + 3.

%e 1/7 = 0.142857... and 7 = 1 + 4 + 2.

%e 1/8 = 0.125 and 8 = 1 + 2 + 5.

%e 1/13 = 0.0769230... and 13 = 7 + 6.

%e 1/14 = 0.0714285... and 14 = 7 + 1 + 4 + 2.

%e 1/34 = 0.02941176470588235... and 34 = 2 + 9 + 4 + 1 + 1 + 7 + 6 + 4.

%Y Cf. A048997.

%K nonn,base

%O 1,1

%A _Anthony Sand_, Jul 01 2014