%I #14 Oct 20 2019 09:03:18

%S 1,4,3,21,2,15,13,12,11,91,9,8,72,7,63,6,56,53,51,48,46,44,42,41,4,38,

%T 36,35,34,33,32,31,3,29,28,271,27,26,251,244,24,233,23,223,22,213,21,

%U 205,201,197,193,19,186,182,18,176,173,17,167,164,162,16,157,154,152

%N a(n) is the smallest k such that the first significant digits of 1/k coincide with n.

%C This sequence differs from A326818 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, in A326818 we assume 1/5 = 0.2000... which leads to A326818(20) = 5, while here we consider 1/5 = 0.2 (without trailing zeros), which leads to a(20) = 48 instead. - _Giovanni Resta_, Oct 20 2019

%e a(36) = 271 because 1/271 = 0.00{36}9003690036900... and 271 is the smallest number with this property.

%t dinv[x_, m_] := Block[{t = If[1 == x/ 2^IntegerExponent[x,2]/ 5^IntegerExponent[x,5], RealDigits[1/x], RealDigits[1/x, 10, m]][[1]]}, If[ Length[t] > m, Take[t, m], t]]; a[n_] := Block[{d = IntegerDigits[n], m, k = 1}, m = Length[d]; While[dinv[k, m] != d, k++]; k]; Array[a, 65] (* _Giovanni Resta_, Oct 20 2019 *)

%Y Cf. A052038, A326818.

%K nonn,base

%O 1,2

%A _Patrick De Geest_, Dec 15 1999