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A368225 Irregular table of nonnegative integers read by rows: the 1's in the binary expansion of n exactly match the nonzero digits in the balanced ternary expansions of the terms in the n-th row.

%I A368225 #16 Dec 19 2023 16:50:03
%S A368225 0,1,3,2,4,9,8,10,6,12,5,7,11,13,27,26,28,24,30,23,25,29,31,18,36,17,
%T A368225 19,35,37,15,21,33,39,14,16,20,22,32,34,38,40,81,80,82,78,84,77,79,83,
%U A368225 85,72,90,71,73,89,91,69,75,87,93,68,70,74,76,86,88,92,94
%N A368225 Irregular table of nonnegative integers read by rows: the 1's in the binary expansion of n exactly match the nonzero digits in the balanced ternary expansions of the terms in the n-th row.
%C A368225 As a flat sequence, this is a permutation of the nonnegative integers with inverse A368226 and infinitely many fixed points (see Formula section).
%C A368225 Row 0 has one term, and for n > 0, row n has A048896(n-1) terms.
%C A368225 For any n >= 0, row n ends with A005836(n+1).
%H A368225 Rémy Sigrist, <a href="/A368225/b368225.txt">Table of n, a(n) for n = 0..9841</a> (rows for n = 0..2^9-1 flattened)
%H A368225 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A368225 A343231(T(n, k)) = n.
%F A368225 a(m) = m for any m in A003462.
%e A368225 Table T(n, k) begins:
%e A368225     0;
%e A368225     1;
%e A368225     3;
%e A368225     2, 4;
%e A368225     9;
%e A368225     8, 10;
%e A368225     6, 12;
%e A368225     5, 7, 11, 13;
%e A368225     27;
%e A368225     26, 28;
%e A368225     24, 30;
%e A368225     23, 25, 29, 31;
%e A368225     18, 36;
%e A368225     17, 19, 35, 37;
%e A368225     15, 21, 33, 39;
%e A368225     14, 16, 20, 22, 32, 34, 38, 40;
%e A368225     81;
%e A368225     ...
%o A368225 (PARI) row(n) = { my (r = [sign(n)], b = binary(n)); for (k = 2, #b, r = [3*v+b[k]|v<-r]; if (b[k], r = concat(r, [v-2|v<-r]););); Set(r); }
%Y A368225 See A368229 and A368239 for similar sequences.
%Y A368225 Cf. A003462, A005836, A048896, A343231, A353662, A368226 (inverse).
%K A368225 nonn,tabf,base
%O A368225 0,3
%A A368225 _Rémy Sigrist_, Dec 18 2023