A326818 a(n) is the smallest k such that the first significant digits of 1/k coincide with n.

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, 36, 35, 34, 33, 32, 31, 3, 29, 28, 271, 27, 26, 251, 25, 24, 233, 23, 223, 22, 213, 21, 205, 201, 2, 193, 19, 186, 182, 18, 176, 173, 17, 167, 164, 162, 16, 157, 154, 152

Offset: 1

Author

Giovanni Resta, Oct 20 2019

Keywords

• nonn
• base

Comments

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.

Examples

			a(123) = 81 because 1/81 = 0.0(123)4... and 81 is the smallest number with this property.
		

Crossrefs

Cf. A052039, A034057.

Programs

Mathematica

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]