A105115 Numbers k such that the decimal representation of 1/k is neither terminating nor purely repeating.

6, 12, 14, 15, 18, 22, 24, 26, 28, 30, 34, 35, 36, 38, 42, 44, 45, 46, 48, 52, 54, 55, 56, 58, 60, 62, 65, 66, 68, 70, 72, 74, 75, 76, 78, 82, 84, 85, 86, 88, 90, 92, 94, 95, 96, 98, 102, 104, 105, 106, 108, 110, 112, 114, 115, 116, 118, 120, 122, 124, 126, 130, 132, 134

Offset: 1

Author

David Wasserman, Apr 07 2005

Keywords

• base
• easy
• nonn

Comments

k is in this sequence iff 1) k is divisible by 2 or 5 and 2) k is also divisible by some prime other than 2 and 5. Contains the numbers that are in neither A003592 nor A045572.

The asymptotic density of this sequence is 3/5. - Amiram Eldar, Mar 26 2021

Examples

			22 is a member because 1/22 = .045454545..., which has a 0 before the repeating 45.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003592, A045572.

Programs

Mathematica

f[n_, lim_] := Block[{g, a}, g[x_] := First /@ FactorInteger@ x; a = g@ n; Select[Range@ lim, And[1 < GCD[#, n] < #, Length@ Complement[g@ #, a] >= 1] &]]; f[10, 134] (* Michael De Vlieger, Jun 20 2015 *)