A361832 For any number k >= 0, let T_k be the triangle whose base corresponds to the ternary expansion of k (without leading zeros) and other values, say t above u and v, satisfy t = (-u-v) mod 3; the 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, 2, 5, 4, 3, 7, 6, 8, 16, 17, 15, 12, 13, 14, 11, 9, 10, 23, 21, 22, 19, 20, 18, 24, 25, 26, 50, 49, 48, 53, 52, 51, 47, 46, 45, 38, 37, 36, 41, 40, 39, 44, 43, 42, 35, 34, 33, 29, 28, 27, 32, 31, 30, 70, 69, 71, 64, 63, 65, 67, 66, 68, 58, 57, 59, 61, 60

Offset

0,3

Comments

This sequence is a variant of A334727.

This sequence is a self-inverse permutation of the nonnegative integers that preserves the number of digits and the leading digit in base 3.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6560

Index entries for sequences related to XOR-triangles

Index entries for sequences that are permutations of the natural numbers

Formula

a(floor(n/3)) = floor(a(n)/3).

a(A004488(n)) = A004488(a(n)).

a(n) = n for any n in A048328.

a(n) = n iff b belongs to A361833.

Example

For n = 42: the ternary expansion of 42 is "1120" and the corresponding triangle is as follows:
       2
      2 2
     1 0 1
    1 1 2 0
So the ternary expansion of a(42) is "1122", and a(42) = 44.

Prog

(PARI) a(n) = { my (d = digits(n, 3), t = vector(#d)); for (k = 1, #d, t[k] = d[1]; d = vector(#d-1, i, (-d[i]-d[i+1]) % 3); ); fromdigits(t, 3); }

Crossrefs

Cf. A004488, A048328, A334727, A361818, A361833 (fixed points).

Sequence in context: A328626 A265357 A265358 * A361945 A171837 A216253

Adjacent sequences: A361829 A361830 A361831 * A361833 A361834 A361835

Keyword

nonn,base

Author

Rémy Sigrist, Mar 26 2023

Status

approved