A372783 In the ternary expansion of n: keep the initial digit, and then replace 0's with 1's and 1's with 0's.

0, 1, 2, 4, 3, 5, 7, 6, 8, 13, 12, 14, 10, 9, 11, 16, 15, 17, 22, 21, 23, 19, 18, 20, 25, 24, 26, 40, 39, 41, 37, 36, 38, 43, 42, 44, 31, 30, 32, 28, 27, 29, 34, 33, 35, 49, 48, 50, 46, 45, 47, 52, 51, 53, 67, 66, 68, 64, 63, 65, 70, 69, 71, 58, 57, 59, 55, 54

Offset: 0

Author

Rémy Sigrist, May 13 2024

Keywords

• nonn
• base
• look
• easy

Comments

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

Examples

			For n = 42: the ternary expansion of 42 is "1120", so the ternary expansion of a(42) is "1021", and a(42) = 34.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A004488, A062318 (fixed points), A115303.

Programs

Mathematica

Table[t3=IntegerDigits[n,3];fd=First[t3];tr=Rest[t3]/.{1->0,0->1};PrependTo[tr,fd];FromDigits[tr,3],{n,0,67}] (* James C. McMahon, May 31 2024 *)

PARI

a(n) = { my (t = digits(n, 3)); for (i = 2, #t, t[i] = [1,0,2][1+t[i]];); fromdigits(t, 3); }

Formula

a(n) = n iff n belongs to A062318.