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A105115 Numbers k such that the decimal representation of 1/k is neither terminating nor purely repeating. 7

%I #18 Mar 26 2021 08:39:25

%S 6,12,14,15,18,22,24,26,28,30,34,35,36,38,42,44,45,46,48,52,54,55,56,

%T 58,60,62,65,66,68,70,72,74,75,76,78,82,84,85,86,88,90,92,94,95,96,98,

%U 102,104,105,106,108,110,112,114,115,116,118,120,122,124,126,130,132,134

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

%C 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.

%C The asymptotic density of this sequence is 3/5. - _Amiram Eldar_, Mar 26 2021

%H Michael De Vlieger, <a href="/A105115/b105115.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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 *)

%Y Cf. A003592, A045572.

%K base,easy,nonn

%O 1,1

%A _David Wasserman_, Apr 07 2005

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)