A371635 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; the balanced ternary expansion of a(n) corresponds to the left border of T_n (the most significant digit being at the bottom left corner).

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

Offset

0,3

Comments

This sequence is a variant of A334727 and A361832.

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9841

Index entries for sequences related to XOR-triangles

Index entries for sequences that are permutations of the natural numbers

Example

For n = 42: the balanced ternary expansion of 42 is "1TTT0" (where T denotes -1), and T_42 is as follows:
         T
        0 1
       1 T 0
      0 T T 1
     1 T T T 0
So the balanced ternary expansion of a(42) is "1010T", and a(42) = 89.

Prog

(PARI) a(n) = { my (b = [], d); while (n, b = concat(d = Mod(n, 3), b); n = (n-centerlift(d)) / 3; ); my (t = vector(#b)); for (i = 1, #t, t[i] = centerlift(b[1]); b = -vector(#b-1, j, b[j]+b[j+1]); ); fromdigits(t, 3); }

Crossrefs

Cf. A334727, A361832, A371636.

Sequence in context: A260596 A265353 A266189 * A368226 A277743 A296099

Adjacent sequences: A371632 A371633 A371634 * A371636 A371637 A371638

Keyword

nonn,base

Author

Rémy Sigrist, Mar 30 2024

Status

approved