A361946 - OEIS

%I #11 Apr 02 2023 10:27:48

%S 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,

%T 31,30,24,25,27,26,32,35,34,33,44,47,46,45,40,43,42,41,36,39,38,37,48,

%U 50,49,51,56,58,57,59,52,54,53,55,60,62,61,63,64,65,67,66

%N 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.

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

%H Rémy Sigrist, <a href="/A361946/b361946.txt">Table of n, a(n) for n = 0..8192</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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

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

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

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

%e For n = 539:

%e - the base-4 expansion of 539 is "20123",

%e - it starts with the digit 2, so we replace 1's by 3's and vice versa,

%e - so the base-4 expansion of a(539) is "20321", and a(539) = 569.

%o (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); }

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

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Apr 01 2023