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

1,2

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.

Links

Table of n, a(n) for n=1..65.

Example

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

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]

Crossrefs

Cf. A052039, A034057.

Sequence in context: A281042 A076589 A275679 * A259229 A052039 A243661

Adjacent sequences: A326815 A326816 A326817 * A326819 A326820 A326821

Keyword

nonn,base

Author

Giovanni Resta, Oct 20 2019

Status

approved