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 A265904 Self-inverse permutation of nonnegative integers: a(n) = A263272(A263273(A263272(n))). 6
 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, 89, 26, 27, 28, 7, 30, 37, 32, 15, 86, 23, 36, 31, 14, 39, 40, 119, 114, 281, 44, 99, 254, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A263273 conjugated with the permutation obtained from its even bisection. LINKS Antti Karttunen, Table of n, a(n) for n = 0..6561 FORMULA a(n) = A263272(A263273(A263272(n))). As a composition of related permutations: a(n) = A263272(A265352(n)). a(n) = A265351(A263272(n)). Other identities. For all n >= 0: a(3*n) = 3*a(n). A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.] MATHEMATICA 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 *) PROG (Scheme) (define (A265904 n) (A263272 (A263273 (A263272 n)))) (Python) from sympy import factorint from sympy.ntheory.factor_ import digits from operator import mul def a030102(n): return 0 if n==0 else int(''.join(map(str, digits(n, 3)[1:][::-1])), 3) def a038502(n):     f=factorint(n)     return 1 if n==1 else reduce(mul, [1 if i==3 else i**f[i] for i in f]) def a038500(n): return n/a038502(n) def a263273(n): return 0 if n==0 else a030102(a038502(n))*a038500(n) def a263272(n): return a263273(2*n)/2 def a(n): return a263272(a263273(a263272(n))) # Indranil Ghosh, May 25 2017 CROSSREFS Cf. A000035, A263272, A263273, A265351, A265352. Cf. also A265902. Cf. A265369, A266190, A266401, A266403 (other conjugates or similar derivations of A263273). Sequence in context: A160652 A131485 A075833 * A117351 A108467 A265565 Adjacent sequences:  A265901 A265902 A265903 * A265905 A265906 A265907 KEYWORD nonn,base AUTHOR Antti Karttunen, Jan 02 2016 STATUS approved

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Last modified June 24 04:38 EDT 2019. Contains 324318 sequences. (Running on oeis4.)