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 A263272 Self-inverse permutation of nonnegative integers: a(n) = A263273(2*n) / 2. 29
 0, 1, 2, 3, 4, 5, 6, 11, 8, 9, 10, 7, 12, 13, 14, 15, 32, 23, 18, 29, 20, 33, 38, 17, 24, 35, 26, 27, 28, 19, 30, 37, 16, 21, 34, 25, 36, 31, 22, 39, 40, 41, 42, 95, 68, 45, 86, 59, 96, 113, 50, 69, 104, 77, 54, 83, 56, 87, 110, 47, 60, 101, 74, 99, 92, 65, 114, 119, 44, 51, 98, 71, 72, 89, 62, 105, 116, 53, 78, 107, 80, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Antti Karttunen, Table of n, a(n) for n = 0..9841 FORMULA a(n) = A263273(2*n) / 2 = A264984(n) / 2. As a composition of related permutations: a(n) = A264974(A264975(n)) = A264976(A264974(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.] A264974(n) = a(2n)/2. [Thus the restriction onto even numbers induces yet another permutation.] 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]]]; Table[f[2 n]/2, {n, 0, 81}] (* Michael De Vlieger, Jan 04 2016, after Jean-François Alcover at A263273 *) PROG (Scheme) (define (A263272 n) (/ (A263273 (+ n n)) 2)) (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 a(n): return a263273(2*n)/2 # Indranil Ghosh, May 23 2017 CROSSREFS Cf. A000035, A263273. Bisections: A264986, A264987. Cf. also A246200, A264967, A264968, A264974, A264978, A264975, A264976, A264984. Sequence in context: A245706 A072622 A072621 * A264968 A264967 A266641 Adjacent sequences:  A263269 A263270 A263271 * A263273 A263274 A263275 KEYWORD nonn,base AUTHOR Antti Karttunen, Dec 05 2015 STATUS approved

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Last modified July 22 16:42 EDT 2019. Contains 325225 sequences. (Running on oeis4.)