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

Author

Rémy Sigrist, Mar 26 2023

Keywords

• nonn
• base

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.

Examples

			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.
		

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

Crossrefs

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

Programs

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); }

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.