A338246 -id:A338246 - cp's OEIS frontend

A338245 Nonnegative values in A117966, in order of appearance.

0, 1, 3, 4, 2, 9, 10, 8, 12, 13, 11, 6, 7, 5, 27, 28, 26, 30, 31, 29, 24, 25, 23, 36, 37, 35, 39, 40, 38, 33, 34, 32, 18, 19, 17, 21, 22, 20, 15, 16, 14, 81, 82, 80, 84, 85, 83, 78, 79, 77, 90, 91, 89, 93, 94, 92, 87, 88, 86, 72, 73, 71, 75, 76, 74, 69, 70, 68

Offset: 0

Rémy Sigrist, Oct 18 2020

This sequence is a permutation of the nonnegative integers with inverse A338247 (the offset has been set to 0 so as to get a permutation).

There are only two fixed points: a(0) = 0 and a(1) = 1.

			A117966 = 0, 1, -1, 3, 4, 2, -3, -2, -4, 9, 10, 8, 12, 13, 11, 6, 7, 5, ...
We keep:  0, 1,     3, 4, 2,             9, 10, 8, 12, 13, 11, 6, 7, 5, ...

See A338248 for a similar sequence.

Cf. A117966, A132141, A338246, A338247.

A117966(n) = subst(Pol(apply(x->if(x == 2, -1, x), digits(n, 3)), 'x), 'x, 3)
print (select(v -> v>=0, apply(A117966, [0..107])))

a(0) = 0.

a(n) = A117966(A132141(n)) for any n > 0.

A371268 If the ternary expansion of n starts with a 1, replace 1's by 2's, 2's by 0's, 0's by 1's, if it starts with a 2, replace 2's by 1's, 1's by 0's, 0's by 2's.

Original entry on oeis.org

0, 2, 1, 7, 8, 6, 5, 3, 4, 22, 23, 21, 25, 26, 24, 19, 20, 18, 17, 15, 16, 11, 9, 10, 14, 12, 13, 67, 68, 66, 70, 71, 69, 64, 65, 63, 76, 77, 75, 79, 80, 78, 73, 74, 72, 58, 59, 57, 61, 62, 60, 55, 56, 54, 53, 51, 52, 47, 45, 46, 50, 48, 49, 35, 33, 34, 29, 27

Offset: 0

Rémy Sigrist, Mar 16 2024

This sequence is a self-inverse permutation of the nonnegative integers.

			The first terms, in decimal and in base 3, are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     2       1          2
   2     1       2          1
   3     7      10         21
   4     8      11         22
   5     6      12         20
   6     5      20         12
   7     3      21         10
   8     4      22         11
   9    22     100        211
  10    23     101        212
  11    21     102        210
  12    25     110        221
  13    26     111        222
  14    24     112        220
  15    19     120        201

See A004488 and A361945 for similar sequences.

Cf. A338246, A371256.

a(n) = { my (d = digits(n, 3)); if (#d, d = if (d[1]==1, apply(v -> [1, 2, 0][1+v], d), apply(v -> [2, 0, 1][1+v], d));); fromdigits(d, 3); }

A371256(a(n)) = A371256(n).

A371636 For any number k >= 0, let T_k be the triangle with values in {-1, 0, +1} whose base corresponds to the balanced ternary expansion of k (without leading zeros) and other values, say t above u and v, satisfy t+u+v = 0 mod 3; this sequence lists the numbers k such that T_k has 3-fold rotational symmetry.

Original entry on oeis.org

0, 1, 4, 13, 19, 25, 40, 103, 112, 121, 154, 214, 364, 442, 505, 595, 673, 763, 826, 913, 1003, 1093, 1144, 1369, 1621, 1915, 2167, 2392, 2776, 3028, 3280, 3628, 4420, 4996, 5668, 6244, 7036, 8203, 9022, 9841, 10459, 10594, 11782, 12304, 13411, 13627, 14419

Offset: 1

Rémy Sigrist, Mar 30 2024

This sequence is a variant of A334556 and A361818.
This sequence is infinite as it contains A003462.
Empirically, for any w > 0, there are A127975(w-1) terms with w balanced ternary digits (ignoring leading zeros).
If k is a term then A338246(k) is also a term.

			The balanced ternary expansion of 595 is "1T11001" (where T denotes -1), and the corresponding triangle T_595 is as follows:
           1
          T 0
         1 0 0
        1 1 T 1
       0 T 0 1 1
      0 0 1 T 0 T
     1 T 1 1 0 0 1
As this triangle has 3-fold rotational symmetry, 595 belongs to the sequence.

Rémy Sigrist, Triangles illustrating initial terms (blue, gray and red respectively denote -1's, 0's and 1's)
Rémy Sigrist, PARI program
Index entries for sequences related to XOR-triangles

Cf. A003462, A127975, A334556, A338246, A361818, A371635.

PARI
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cp's OEIS Frontend

A338245 Nonnegative values in A117966, in order of appearance.

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A371268 If the ternary expansion of n starts with a 1, replace 1's by 2's, 2's by 0's, 0's by 1's, if it starts with a 2, replace 2's by 1's, 1's by 0's, 0's by 2's.

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