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A265904 Self-inverse permutation of nonnegative integers: a(n) = A263272(A263273(A263272(n))).

%I A265904 #15 May 25 2017 03:17:22
%S A265904 0,1,2,3,4,11,6,29,8,9,10,5,12,13,38,33,92,17,18,83,20,87,110,35,24,
%T A265904 89,26,27,28,7,30,37,32,15,86,23,36,31,14,39,40,119,114,281,44,99,254,
%U A265904 65,276,335,98,51,260,71,54,245,56,249,326,101,60,263,74,261,272,47,330,353,116,105,278,53,72,251,62,267,332,107,78,269,80,81,82,19
%N A265904 Self-inverse permutation of nonnegative integers: a(n) = A263272(A263273(A263272(n))).
%C A265904 A263273 conjugated with the permutation obtained from its even bisection.
%H A265904 Antti Karttunen, <a href="/A265904/b265904.txt">Table of n, a(n) for n = 0..6561</a>
%H A265904 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A265904 a(n) = A263272(A263273(A263272(n))).
%F A265904 As a composition of related permutations:
%F A265904 a(n) = A263272(A265352(n)).
%F A265904 a(n) = A265351(A263272(n)).
%F A265904 Other identities. For all n >= 0:
%F A265904 a(3*n) = 3*a(n).
%F A265904 A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
%t A265904 f[n_] := Block[{g, h}, g[x_] := x/3^IntegerExponent[x, 3]; h[x_] := x/g@ x; If[n == 0, 0, FromDigits[Reverse@ IntegerDigits[#, 3], 3] &@g[n] h[n]]]; t = Table[f[2 n]/2, {n, 0, 1000}]; Table[t[[f[t[[n + 1]]] + 1]], {n, 0, 83}] (* _Michael De Vlieger_, Jan 04 2016, after _Jean-François Alcover_ at A263273 *)
%o A265904 (Scheme) (define (A265904 n) (A263272 (A263273 (A263272 n))))
%o A265904 (Python)
%o A265904 from sympy import factorint
%o A265904 from sympy.ntheory.factor_ import digits
%o A265904 from operator import mul
%o A265904 def a030102(n): return 0 if n==0 else int(''.join(map(str, digits(n, 3)[1:][::-1])), 3)
%o A265904 def a038502(n):
%o A265904     f=factorint(n)
%o A265904     return 1 if n==1 else reduce(mul, [1 if i==3 else i**f[i] for i in f])
%o A265904 def a038500(n): return n/a038502(n)
%o A265904 def a263273(n): return 0 if n==0 else a030102(a038502(n))*a038500(n)
%o A265904 def a263272(n): return a263273(2*n)/2
%o A265904 def a(n): return a263272(a263273(a263272(n))) # _Indranil Ghosh_, May 25 2017
%Y A265904 Cf. A000035, A263272, A263273, A265351, A265352.
%Y A265904 Cf. also A265902.
%Y A265904 Cf. A265369, A266190, A266401, A266403 (other conjugates or similar derivations of A263273).
%K A265904 nonn,base
%O A265904 0,3
%A A265904 _Antti Karttunen_, Jan 02 2016