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A052039
a(n) is the smallest k such that the first significant digits of 1/k coincide with n.
3
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, 36, 35, 34, 33, 32, 31, 3, 29, 28, 271, 27, 26, 251, 244, 24, 233, 23, 223, 22, 213, 21, 205, 201, 197, 193, 19, 186, 182, 18, 176, 173, 17, 167, 164, 162, 16, 157, 154, 152
OFFSET
1,2
COMMENTS
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
EXAMPLE
a(36) = 271 because 1/271 = 0.00{36}9003690036900... and 271 is the smallest number with this property.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A275679 A326818 A259229 * A243661 A035048 A192857
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Dec 15 1999
STATUS
approved