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A110081 Integers n such that the digit set D = (0, 1, -n) used in base 3 expansions of the form Sum_{ -N < j < oo} d_j 3^{-j}, all d_j in D, can represent all real numbers.

%I A110081 #36 Oct 22 2022 16:20:11
%S A110081 1,7,25,31,37,73,79,85,97,103,193,241,253,271,313,319,337,343,361,517,
%T A110081 553,661,703,721,727,733,745,751,781,799,805,865,925,943,967,1015,
%U A110081 1039,1081,1087,1633,1687,1705,1837,1981,2125,2137,2143,2185,2191,2233,2257,2263,2341,2581,2593,2605,2641,2719,2761,2797,2815,2833,2857,2887,2893,2911,3127
%N A110081 Integers n such that the digit set D = (0, 1, -n) used in base 3 expansions of the form Sum_{ -N < j < oo} d_j 3^{-j}, all d_j in D, can represent all real numbers.
%C A110081 All nonnegative reals can be represented with ternary digits 0, 1, 2. If you're not allowed to use 2, then you only get something like the Cantor set. But you're back in business if you're allowed to use 0, 1, -1 - this gives the "balanced" ternary representation (so 1 is in the sequence).
%C A110081 The sequence is known to be infinite and irregular and is conjectured to have density zero.
%D A110081 J. C. Lagarias, Crystals, Tilings and Packings, Hedrick Lectures, Math. Assoc. America MathFest, 2005.
%H A110081 Joerg Arndt, <a href="/A110081/b110081.txt">Table of n, a(n) for n = 1..1000</a>
%H A110081 David W. Matula, <a href="http://dx.doi.org/10.1145/322344.322355">Basic digit sets for radix representation</a>, J. Assoc. Comput. Mach. 29 (1982), 1131-1143.
%H A110081 Don Reble, <a href="/A110081/a110081.txt">Python Program</a>
%e A110081 13/18 = 0.122111111111... in ternary which can't be represented without the 2's. But it is 10.x0111111111... if x = -7: 3 + 0 + (-7)/3 + 1/3^3 + 1/3^4 + 1/3^5 + ... = 3 - 7/3 + (1/27)/(1-(1/3)) = 13/18.
%K A110081 nonn,base,nice
%O A110081 1,2
%A A110081 _N. J. A. Sloane_, based on correspondence from _R. K. Guy_ and Jeff Lagarias, Aug 31 2005
%E A110081 More terms using _Don Reble_'s program from _Joerg Arndt_, Sep 17 2017