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A265369 Self-inverse permutation of nonnegative integers: a(n) = A057889(A263273(A057889(n))).

%I A265369 #13 May 23 2017 20:59:47
%S A265369 0,1,2,3,4,7,6,5,8,9,10,11,12,25,26,21,16,19,18,17,20,15,22,59,24,13,
%T A265369 14,27,28,29,30,41,64,39,58,53,36,97,98,33,40,31,66,121,44,63,50,61,
%U A265369 48,73,46,105,100,35,54,65,56,57,34,23,60,47,82,45,32,55,42,137,68,69,142,131,72,49,74,219,76,155,234,79,80,81,62,173
%N A265369 Self-inverse permutation of nonnegative integers: a(n) = A057889(A263273(A057889(n))).
%H A265369 Antti Karttunen, <a href="/A265369/b265369.txt">Table of n, a(n) for n = 0..19684</a>
%H A265369 Indranil Ghosh, <a href="/A265369/a265369.txt">Python program to generate the sequence</a>
%H A265369 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A265369 a(n) = A057889(A263273(A057889(n))).
%F A265369 As a composition of related permutations:
%F A265369 a(n) = A264966(A057889(n)).
%F A265369 a(n) = A057889(A264965(n)).
%F A265369 Other identities. For all n >= 0:
%F A265369 A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
%t A265369 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[g@ f@ g@ n, {n, 83}] (* _Michael De Vlieger_, Jan 04 2016, after _Jean-François Alcover_ at A263273 and _Ivan Neretin_ at A057889 *)
%o A265369 (Scheme) (define (A265369 n) (A057889 (A263273 (A057889 n))))
%Y A265369 Cf. A000035, A057889, A263273, A264965, A264966.
%Y A265369 Cf. also A265329, A265904, A266190, A266401, A266403, A266407, A266408.
%K A265369 nonn,base
%O A265369 0,3
%A A265369 _Antti Karttunen_, Jan 02 2016