A035335 a(n) = smallest number m such that n appears in decimal expansion of 1/m.

6, 4, 3, 7, 2, 6, 7, 7, 11, 10, 9, 8, 23, 7, 19, 6, 17, 49, 21, 5, 19, 31, 13, 29, 4, 19, 29, 7, 17, 13, 19, 31, 3, 23, 17, 19, 27, 26, 23, 25, 17, 7, 23, 29, 22, 26, 17, 29, 51, 2, 29, 17, 26, 22, 18, 23, 7, 17, 47, 23, 21, 16, 19, 17, 23, 6, 49, 19, 13, 17, 7, 29, 19, 47, 29, 13

Offset: 1

Author

Erich Friedman

Keywords

• easy
• nice
• nonn
• base
• look

Examples

			a(13)=23 since 1/23=.04347826086956521739{13}... is the first to contain 13.
1/6=.16666... so a(n)=6 for n=1,6,16,66,166,666,1666,6666, ...
		

Links

• David W. Wilson, Table of n, a(n) for n = 1..10000 (n <= 200 from R. J. Mathar)

Programs

Mathematica

foundQ[n_, m_] := (idn = IntegerDigits[n]; ln = Length[idn]; rdm = Most[ Flatten[ RealDigits[1/m, 10, lm = 2* Length[ Flatten[ RealDigits[1/m]]]]]]; found = False; Do[If[idn === Take[rdm, {k, k+ln-1}], found = True; Break[]], {k, 1, lm-ln+1}]; found); a[n_] := (m = 2; While[ True, If[foundQ[n, m], Break[], m++]]; m); a[n_ /; n > 1 && IntegerQ[ Log[10, n]]] := 10; a[n_ /; n > 1 && Union[ IntegerDigits[n]] == {1}] := 9; Table[a[n], {n, 1, 76}] (* Jean-François Alcover, Oct 24 2011 *)
Table[Function[r, SelectFirst[Range[2, 10^3], Length@ SequencePosition[ If[Depth@ # == 3, Flatten@ Join[#, Table[Last@ #, Length@ # + Length@ r]], PadRight[#, Length@ # + Length@ r]] &@ First@ RealDigits[1/#], r] > 0 &]]@ IntegerDigits@ n, {n, 120}] (* Michael De Vlieger, May 14 2016, Version 10.1 *)