A052039 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, 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

Links

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

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

Cf. A052038, A326818.

Sequence in context: A275679 A326818 A259229 * A243661 A035048 A192857

Adjacent sequences: A052036 A052037 A052038 * A052040 A052041 A052042

Keyword

nonn,base

Author

Patrick De Geest, Dec 15 1999

Status

approved