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A371276 Nonnegative numbers whose balanced ternary expansions have no consecutive equal digits (with offset 0).

%I A371276 #10 Mar 18 2024 13:24:09
%S A371276 0,1,2,3,6,7,8,10,17,19,20,21,24,25,29,30,51,52,56,57,60,61,62,64,71,
%T A371276 73,74,75,87,88,89,91,152,154,155,156,168,169,170,172,179,181,182,183,
%U A371276 186,187,191,192,213,214,218,219,222,223,224,226,260,262,263,264
%N A371276 Nonnegative numbers whose balanced ternary expansions have no consecutive equal digits (with offset 0).
%C A371276 Although this is a list, we use an offset equal to 0; thus:
%C A371276 - the binary expansion of n has the same number of digits as the balanced ternary expansion of a(n) (ignoring leading zeros),
%C A371276 - for n > 0 with binary expansion (b_1, ..., b_w) (where b_1 = 1), let's say that the balanced ternary expansion of a(n) is (t_1, ..., t_w) (where t_1 = 1):
%C A371276     - for i = 2..w:
%C A371276         - if b_i = 0, then t_i = min({-1, 0, +1} \ {t_{i-1}}),
%C A371276         - otherwise, t_i = max({-1, 0, +1} \ {t_{i-1}}).
%C A371276 For any w > 0, there are 2^(w-1) positive terms with w balanced ternary digits.
%H A371276 Rémy Sigrist, <a href="/A371276/b371276.txt">Table of n, a(n) for n = 0..8191</a>
%e A371276 The first terms, alongside their balanced ternary expansions, are:
%e A371276   n   a(n)  bter(a(n))
%e A371276   --  ----  ----------
%e A371276    1     0           0
%e A371276    2     1           1
%e A371276    3     2          1T
%e A371276    4     3          10
%e A371276    5     6         1T0
%e A371276    6     7         1T1
%e A371276    7     8         10T
%e A371276    8    10         101
%e A371276    9    17        1T0T
%e A371276   10    19        1T01
%e A371276   11    20        1T1T
%e A371276   12    21        1T10
%e A371276   13    24        10T0
%e A371276   14    25        10T1
%e A371276   15    29        101T
%e A371276   16    30        1010
%o A371276 (PARI) is(n) = { while (n, my (d = centerlift(Mod(n, 3))); n = (n-d)/3; if (d==centerlift(Mod(n, 3)), return (0););); return (1); }
%o A371276 (PARI) a(n) = { my (d = binary(n)); for (i = 2, #d, d[i] = setminus([-1,0,1], [d[i-1]])[1+d[i]];); fromdigits(d, 3); }
%Y A371276 See A031941 for a similar sequence.
%Y A371276 Cf. A134021.
%K A371276 nonn,base
%O A371276 0,3
%A A371276 _Rémy Sigrist_, Mar 17 2024