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a(n) = n if n < 4, otherwise 4*a(floor(n/4)) + 3 - n mod 4.
10

%I #17 Jun 01 2024 14:53:16

%S 1,2,3,7,6,5,4,11,10,9,8,15,14,13,12,31,30,29,28,27,26,25,24,23,22,21,

%T 20,19,18,17,16,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,63,62,

%U 61,60,59,58,57,56,55,54,53,52,51,50,49,48,127,126,125,124,123,122,121

%N a(n) = n if n < 4, otherwise 4*a(floor(n/4)) + 3 - n mod 4.

%C Self-inverse permutation of the natural numbers.

%C If n is written in base-4 representation, then a(n) is the value after replacing all digits d (except for the leading one) by 3-d.

%H Paolo Xausa, <a href="/A115304/b115304.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A115310(n+2,3).

%t A115304[n_] := FromDigits[MapAt[3 - # &, IntegerDigits[n, 4], 2;;], 4];

%t Array[A115304, 100] (* _Paolo Xausa_, May 20 2024 *)

%Y Cf. A054429, A115303, A115305, A115306, A115307, A115308, A115309, A106649.

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, Jan 20 2006