A361946 If the base-4 expansion of n starts with the digit 1, then replace 2's by 3's and vice versa; if it starts with the digit 2, then replace 1's by 3's and vice versa; if it starts with the digit 3, then replace 1's by 2's and vice versa; a(0) = 0.

0, 1, 2, 3, 4, 5, 7, 6, 8, 11, 10, 9, 12, 14, 13, 15, 16, 17, 19, 18, 20, 21, 23, 22, 28, 29, 31, 30, 24, 25, 27, 26, 32, 35, 34, 33, 44, 47, 46, 45, 40, 43, 42, 41, 36, 39, 38, 37, 48, 50, 49, 51, 56, 58, 57, 59, 52, 54, 53, 55, 60, 62, 61, 63, 64, 65, 67, 66

Offset: 0

Author

Rémy Sigrist, Apr 01 2023

Keywords

• nonn
• base

Comments

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

Examples

			For n = 539:
- the base-4 expansion of 539 is "20123",
- it starts with the digit 2, so we replace 1's by 3's and vice versa,
- so the base-4 expansion of a(539) is "20321", and a(539) = 569.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000695, A048647, A057300, A122587, A163241, A361945, A361947.

Programs

PARI

a(n) = { my (q = digits(n, 4), m = if (#q, [ [0,1,3,2], [0,3,2,1], [0,2,1,3] ][q[1]], [0,1,2,3])); fromdigits(apply (d -> m[1+d], q), 4); }

Formula

a(n) = A163241(n) when A122587(n) = 1.

a(n) = A048647(n) when A122587(n) = 2.

a(n) = A057300(n) when A122587(n) = 3.

a(n) = n iff n = d * A000695(k) for some d in {1, 2, 3} and some k >= 0.