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A265329 Self-inverse permutation of nonnegative integers: a(n) = A263273(A057889(A263273(n))).

%I A265329 #15 May 25 2017 03:16:51
%S A265329 0,1,2,3,4,5,6,7,8,9,10,17,12,19,26,15,16,11,18,13,20,21,22,55,24,25,
%T A265329 14,27,28,65,30,67,32,39,38,35,36,37,34,33,40,145,42,73,100,45,46,61,
%U A265329 48,79,226,219,76,121,54,23,56,57,70,59,60,47,82,63,64,29,66,31,68,81,58,217,72,43,74,75,52,193,174,49,80,69,62,221
%N A265329 Self-inverse permutation of nonnegative integers: a(n) = A263273(A057889(A263273(n))).
%H A265329 Antti Karttunen, <a href="/A265329/b265329.txt">Table of n, a(n) for n = 0..16384</a>
%H A265329 Indranil Ghosh, <a href="/A265329/a265329.txt">Python program to generate the sequence</a>
%H A265329 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A265329 a(n) = A263273(A057889(A263273(n))).
%F A265329 As a composition of related permutations:
%F A265329 a(n) = A264965(A263273(n)).
%F A265329 a(n) = A263273(A264966(n)).
%F A265329 Other identities. For all n >= 0:
%F A265329 A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
%t A265329 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]]]; g[n_] := FromDigits[Reverse@ IntegerDigits[n, 2], 2] 2^IntegerExponent[n, 2]; Prepend[#, 0] &@ Table[f@ g@ f@ n, {n, 83}] (* _Michael De Vlieger_, Jan 04 2016, after _Jean-François Alcover_ at A263273 and _Ivan Neretin_ at A057889 *)
%o A265329 (Scheme) (define (A265329 n) (A263273 (A057889 (A263273 n))))
%Y A265329 Cf. A000035, A057889, A263273, A264965, A264966.
%Y A265329 Cf. A266402, A266404.
%Y A265329 Cf. also A265369.
%K A265329 nonn,base
%O A265329 0,3
%A A265329 _Antti Karttunen_, Jan 02 2016