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

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base

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

Examples

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

Crossrefs

Cf. A052038, A326818.

Programs

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 *)