A263272 Self-inverse permutation of nonnegative integers: a(n) = A263273(2*n) / 2.
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
Offset: 0
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Crossrefs
Programs
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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 *) -
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 -
Scheme
(define (A263272 n) (/ (A263273 (+ n n)) 2))
Formula
As a composition of related permutations:
Other identities. For all n >= 0:
a(3*n) = 3*a(n).
A264974(n) = a(2n)/2. [Thus the restriction onto even numbers induces yet another permutation.]
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