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%I #29 May 03 2020 06:02:51
%S 0,0,1,0,0,1,2,2,3,0,0,1,0,0,1,2,2,3,4,4,5,4,4,5,6,6,7,0,0,1,0,0,1,2,
%T 2,3,0,0,1,0,0,1,2,2,3,4,4,5,4,4,5,6,6,7,8,8,9,8,8,9,10,10,11,8,8,9,8,
%U 8,9,10,10,11,12,12,13,12,12,13,14,14,15,0
%N A binary encoding of the twos in ternary representation of n (see Comments for precise definition).
%C The ones in the binary representation of a(n) correspond to the twos in the ternary representation of n; for example: ternary(42) = 1120 and binary(a(42)) = 10 (a(42) = 2).
%C See A289813 for the sequence encoding the ones in ternary representation of n and additional comments.
%H Rémy Sigrist, <a href="/A289814/b289814.txt">Table of n, a(n) for n = 0..6560</a>
%F a(0) = 0.
%F a(3*n) = 2 * a(n).
%F a(3*n+1) = 2 * a(n).
%F a(3*n+2) = 2 * a(n) + 1.
%F Also, a(n) = A289813(A004488(n)).
%F A053735(n) = A000120(A289813(n)) + 2*A000120(a(n)). - _Antti Karttunen_, Jul 20 2017
%e The first values, alongside the ternary representation of n, and the binary representation of a(n), are:
%e n a(n) ternary(n) binary(a(n))
%e -- ---- ---------- ------------
%e 0 0 0 0
%e 1 0 1 0
%e 2 1 2 1
%e 3 0 10 0
%e 4 0 11 0
%e 5 1 12 1
%e 6 2 20 10
%e 7 2 21 10
%e 8 3 22 11
%e 9 0 100 0
%e 10 0 101 0
%e 11 1 102 1
%e 12 0 110 0
%e 13 0 111 0
%e 14 1 112 1
%e 15 2 120 10
%e 16 2 121 10
%e 17 3 122 11
%e 18 4 200 100
%e 19 4 201 100
%e 20 5 202 101
%e 21 4 210 100
%e 22 4 211 100
%e 23 5 212 101
%e 24 6 220 110
%e 25 6 221 110
%e 26 7 222 111
%t Table[FromDigits[#, 2] &[IntegerDigits[n, 3] /. d_ /; d > 0 :> d - 1], {n, 0, 81}] (* _Michael De Vlieger_, Jul 20 2017 *)
%o (PARI) a(n) = my (d=digits(n,3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2)
%o (Python)
%o from sympy.ntheory.factor_ import digits
%o def a(n):
%o d = digits(n, 3)[1:]
%o return int("".join('1' if i == 2 else '0' for i in d), 2)
%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jul 20 2017
%Y Cf. A000120, A053735, A289813.
%K nonn,base,look
%O 0,7
%A _Rémy Sigrist_, Jul 12 2017
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