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

1,1

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A003592, A045572.

Sequence in context: A348551 A143957 A318981 * A366532 A325700 A360551

Adjacent sequences: A105112 A105113 A105114 * A105116 A105117 A105118

Keyword

base,easy,nonn

Author

David Wasserman, Apr 07 2005

Status

approved