This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289814 #33 May 09 2024 03:12:18
%S A289814 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 A289814 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 A289814 8,9,10,10,11,12,12,13,12,12,13,14,14,15,0
%N A289814 A binary encoding of the twos in ternary representation of n (see Comments for precise definition).
%C A289814 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 A289814 See A289813 for the sequence encoding the ones in ternary representation of n and additional comments.
%H A289814 Rémy Sigrist, <a href="/A289814/b289814.txt">Table of n, a(n) for n = 0..6560</a>
%F A289814 a(0) = 0.
%F A289814 a(3*n) = 2 * a(n).
%F A289814 a(3*n+1) = 2 * a(n).
%F A289814 a(3*n+2) = 2 * a(n) + 1.
%F A289814 Also, a(n) = A289813(A004488(n)).
%F A289814 A053735(n) = A000120(A289813(n)) + 2*A000120(a(n)). - _Antti Karttunen_, Jul 20 2017
%e A289814 The first values, alongside the ternary representation of n, and the binary representation of a(n), are:
%e A289814 n a(n) ternary(n) binary(a(n))
%e A289814 -- ---- ---------- ------------
%e A289814 0 0 0 0
%e A289814 1 0 1 0
%e A289814 2 1 2 1
%e A289814 3 0 10 0
%e A289814 4 0 11 0
%e A289814 5 1 12 1
%e A289814 6 2 20 10
%e A289814 7 2 21 10
%e A289814 8 3 22 11
%e A289814 9 0 100 0
%e A289814 10 0 101 0
%e A289814 11 1 102 1
%e A289814 12 0 110 0
%e A289814 13 0 111 0
%e A289814 14 1 112 1
%e A289814 15 2 120 10
%e A289814 16 2 121 10
%e A289814 17 3 122 11
%e A289814 18 4 200 100
%e A289814 19 4 201 100
%e A289814 20 5 202 101
%e A289814 21 4 210 100
%e A289814 22 4 211 100
%e A289814 23 5 212 101
%e A289814 24 6 220 110
%e A289814 25 6 221 110
%e A289814 26 7 222 111
%t A289814 Table[FromDigits[#, 2] &[IntegerDigits[n, 3] /. d_ /; d > 0 :> d - 1], {n, 0, 81}] (* _Michael De Vlieger_, Jul 20 2017 *)
%o A289814 (PARI) a(n) = my (d=digits(n,3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2)
%o A289814 (PARI) a(n) = fromdigits(digits(n, 3)\2, 2); \\ _Ruud H.G. van Tol_, May 08 2024
%o A289814 (Python)
%o A289814 from sympy.ntheory.factor_ import digits
%o A289814 def a(n):
%o A289814 d = digits(n, 3)[1:]
%o A289814 return int("".join('1' if i == 2 else '0' for i in d), 2)
%o A289814 print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jul 20 2017
%Y A289814 Cf. A000120, A053735, A289813.
%K A289814 nonn,base,look
%O A289814 0,7
%A A289814 _Rémy Sigrist_, Jul 12 2017