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A213912 a(1) = 1; for n>1, a(n) = floor(sqrt(a(n-1))) if that number is not already in the sequence, otherwise a(n) = 3*a(n-1).

%I A213912 #12 Jun 27 2020 03:05:24
%S A213912 1,3,9,27,5,2,6,18,4,12,36,108,10,30,90,270,16,48,144,432,20,60,7,21,
%T A213912 63,189,13,39,117,351,1053,32,96,288,864,29,87,261,783,2349,7047,83,
%U A213912 249,15,45,135,11,33,99,297,17,51,153,459,1377,37,111,333,999,31
%N A213912 a(1) = 1; for n>1, a(n) = floor(sqrt(a(n-1))) if that number is not already in the sequence, otherwise a(n) = 3*a(n-1).
%C A213912 Permutation of natural numbers with inverse A213913.
%H A213912 Reinhard Zumkeller, <a href="/A213912/b213912.txt">Table of n, a(n) for n = 1..10000</a>
%H A213912 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A213912 (Haskell)
%o A213912 a213912 n = a213912_list !! (n-1)
%o A213912 a213912_list = 1 : f [1] where
%o A213912    f xs@(x:_) = y : f (y : xs) where
%o A213912      y = if z `notElem` xs then z else 3 * x where z = a000196 x
%o A213912 (PARI) lista(nn) = {my(k, v=vector(nn)); v[1]=1; for(n=2, nn, if(vecsearch(vecsort(v), k=sqrtint(v[n-1])), v[n]=3*v[n-1], v[n]=k)); v; } \\ _Jinyuan Wang_, Jun 26 2020
%Y A213912 Cf. A114183.
%K A213912 nonn,look
%O A213912 1,2
%A A213912 _Reinhard Zumkeller_, Mar 05 2013