A115303 - OEIS

%I #22 May 24 2024 08:41:21

%S 1,2,5,4,3,8,7,6,17,16,15,14,13,12,11,10,9,26,25,24,23,22,21,20,19,18,

%T 53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,

%U 30,29,28,27,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62

%N a(n) = n if n < 3, otherwise 3*a(floor(n/3)) + 2 - n mod 3.

%C Self-inverse permutation of the natural numbers.

%C if n is written in ternary representation, then a(n) is the value after replacing all digits d (but not the leading one) with 2-d.

%C a(n+1) = a(n)-1 unless n = 3^k - 1 or 2*3^k-1 for some k. - _Robert Israel_, Feb 28 2023

%H Robert Israel, <a href="/A115303/b115303.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+1,2).

%p a:= proc(n) option remember;

%p    3*procname(floor(n/3))+2 - (n mod 3)

%p end proc:

%p a(1):= 1: a(2):= 2:

%p map(a, [$1..100]); # _Robert Israel_, Feb 28 2023

%t A115303[n_] := FromDigits[MapAt[2 - # &, IntegerDigits[n, 3], 2;;], 3];

%t Array[A115303, 100] (* _Paolo Xausa_, May 20 2024 *)

%Y Cf. A054429, A115304, A115305, A115306, A115307, A115308, A115309, A106649.

%K nonn,base,look

%O 1,2

%A _Reinhard Zumkeller_, Jan 20 2006