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 A289813 A binary encoding of the ones in ternary representation of n (see Comments for precise definition). 30
 0, 1, 0, 2, 3, 2, 0, 1, 0, 4, 5, 4, 6, 7, 6, 4, 5, 4, 0, 1, 0, 2, 3, 2, 0, 1, 0, 8, 9, 8, 10, 11, 10, 8, 9, 8, 12, 13, 12, 14, 15, 14, 12, 13, 12, 8, 9, 8, 10, 11, 10, 8, 9, 8, 0, 1, 0, 2, 3, 2, 0, 1, 0, 4, 5, 4, 6, 7, 6, 4, 5, 4, 0, 1, 0, 2, 3, 2, 0, 1, 0, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The ones in the binary representation of a(n) correspond to the ones in the ternary representation of n; for example: ternary(42) = 1120 and binary(a(42)) = 1100 (a(42) = 12). See A289814 for the sequence encoding the twos in ternary representation of n. By design, a(n) AND A289814(n) = 0 (where AND stands for the bitwise AND operator). See A289831 for the sum of this sequence and A289814. For each pair of numbers without common bits in base 2 representation, say x and y, there is a unique index, say n, such that a(n) = x and A289814(n) = y; in fact, n = A289869(x,y). The scatterplot of this sequence vs A289814 looks like a Sierpinski triangle pivoted to the side. For any t > 0: we can adapt the algorithm used here and in A289814 in order to uniquely enumerate every tuple of t numbers mutually without common bits in base 2 representation. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..6560 FORMULA a(0) = 0. a(3*n) = 2 * a(n). a(3*n+1) = 2 * a(n) + 1. a(3*n+2) = 2 * a(n). Also, a(n) = A289814(A004488(n)). A053735(n) = A000120(a(n)) + 2*A000120(A289814(n)). - Antti Karttunen, Jul 20 2017 EXAMPLE The first values, alongside the ternary representation of n, and the binary repesentation of a(n), are: n       a(n)    ternary(n)  binary(a(n)) --      ----    ----------  ------------ 0       0       0           0 1       1       1           1 2       0       2           0 3       2       10          10 4       3       11          11 5       2       12          10 6       0       20          0 7       1       21          1 8       0       22          0 9       4       100         100 10      5       101         101 11      4       102         100 12      6       110         110 13      7       111         111 14      6       112         110 15      4       120         100 16      5       121         101 17      4       122         100 18      0       200         0 19      1       201         1 20      0       202         0 21      2       210         10 22      3       211         11 23      2       212         10 24      0       220         0 25      1       221         1 26      0       222         0 MATHEMATICA Table[FromDigits[#, 2] &[IntegerDigits[n, 3] /. 2 -> 0], {n, 0, 81}] (* Michael De Vlieger, Jul 20 2017 *) PROG (PARI) a(n) = my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2) (Python) from sympy.ntheory.factor_ import digits def a(n):     d=digits(n, 3)[1:]     return int("".join(['1' if i==1 else '0' for i in d]), 2) print map(a, xrange(101)) # Indranil Ghosh, Jul 20 2017 CROSSREFS Cf. A000120, A004488, A005836, A053735, A289814, A289831, A289869. Sequence in context: A100219 A079757 A071493 * A050075 A247490 A002120 Adjacent sequences:  A289810 A289811 A289812 * A289814 A289815 A289816 KEYWORD nonn,base,look AUTHOR Rémy Sigrist, Jul 12 2017 STATUS approved

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Last modified January 21 19:59 EST 2019. Contains 319350 sequences. (Running on oeis4.)