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%I #14 Mar 15 2021 08:13:43
%S 1,4,3,21,2,15,13,12,11,1,9,8,72,7,63,6,56,53,51,5,46,44,42,41,4,38,
%T 36,35,34,33,32,31,3,29,28,271,27,26,251,25,24,233,23,223,22,213,21,
%U 205,201,2,193,19,186,182,18,176,173,17,167,164,162,16,157,154,152
%N a(n) is the smallest k such that the first significant digits of 1/k coincide with n.
%C This sequence differs from A052039 in how it treats reciprocals with terminating representation, i.e., the values 1/k for integers k whose prime factors are 2 and/or 5. For example, here we assume 1/5 = 0.2000... which leads to a(20) = 5, while in A052039 we consider 1/5 = 0.2 (without trailing zeros), which leads to A052039(20) = 48 instead.
%e a(123) = 81 because 1/81 = 0.0(123)4... and 81 is the smallest number with this property.
%t a[n_] := Block[{d = IntegerDigits[n], m, k = 1}, m = Length[d]; While[ RealDigits[1/k, 10, m][[1]] != d, k++]; k]; Array[a, 65]
%Y Cf. A052039, A034057.
%K nonn,base
%O 1,2
%A _Giovanni Resta_, Oct 20 2019
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