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A266189 Self-inverse permutation of nonnegative integers: a(n) = A263273(A264985(A263273(n))). 3
0, 1, 3, 2, 4, 10, 6, 9, 12, 7, 5, 11, 8, 13, 37, 24, 28, 31, 21, 19, 57, 18, 27, 30, 15, 36, 39, 22, 16, 34, 23, 17, 35, 69, 29, 32, 25, 14, 38, 26, 40, 118, 78, 109, 112, 75, 46, 100, 72, 82, 91, 51, 85, 94, 66, 64, 192, 20, 73, 219, 60, 171, 138, 63, 55, 165, 54, 81, 84, 33, 90, 111, 48, 58, 174, 45, 108, 93, 42, 117, 120, 67, 49 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..6561

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A263273(A264985(A263273(n))).

As a composition of related permutations:

a(n) = A263273(A265353(n)).

a(n) = A265354(A263273(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]]]; s = Select[f /@ Range@ 5000, OddQ]; t = Table[(s[[n + 1]] - 1)/2, {n, 0, 1000}]; Table[f@ t[[f@ n + 1]], {n, 0, 82}] (* Michael De Vlieger, Jan 04 2016, after Jean-Fran├žois Alcover at A263273 *)

PROG

(Scheme) (define (A266189 n) (A263273 (A264985 (A263273 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 a264985(n): return (a263273(2*n + 1) - 1)/2

def a(n): return a263273(a264985(a263273(n))) # Indranil Ghosh, May 22 2017

CROSSREFS

Cf. A263273, A264985, A265353, A265354.

Cf. also A265902, A266190.

Sequence in context: A095259 A260596 A265353 * A277743 A296099 A319103

Adjacent sequences:  A266186 A266187 A266188 * A266190 A266191 A266192

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Jan 02 2016

STATUS

approved

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)