A264985 - OEIS

%I #17 May 22 2017 20:07:49

%S 0,1,3,2,4,9,6,10,12,5,7,11,8,13,27,18,28,36,15,19,33,24,31,30,21,37,

%T 39,14,16,32,23,22,29,20,34,38,17,25,35,26,40,81,54,82,108,45,55,99,

%U 72,85,90,63,109,117,42,46,96,69,58,87,60,100,114,51,73,105,78,94,84,57,91,111,48,64,102,75,112,93,66,118,120,41

%N Self-inverse permutation of nonnegative integers: a(n) = (A264983(n)-1) / 2.

%H Antti Karttunen, <a href="/A264985/b264985.txt">Table of n, a(n) for n = 0..9841</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = (A264983(n)-1) / 2 = (1/2) * (A263273(2n + 1) - 1).

%t 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 = Select[f /@ Range@ 1000, OddQ]; Table[(t[[n + 1]] - 1)/2, {n, 0, 81}] (* _Michael De Vlieger_, Jan 04 2016, after _Jean-François Alcover_ at A263273 *)

%o (Scheme) (define (A264985 n) (/ (- (A264983 n) 1) 2))

%o (Python)

%o from sympy import factorint

%o from sympy.ntheory.factor_ import digits

%o from operator import mul

%o def a030102(n): return 0 if n==0 else int(''.join(map(str, digits(n, 3)[1:][::-1])), 3)

%o def a038502(n):

%o     f=factorint(n)

%o     return 1 if n==1 else reduce(mul, [1 if i==3 else i**f[i] for i in f])

%o def a038500(n): return n/a038502(n)

%o def a263273(n): return 0 if n==0 else a030102(a038502(n))*a038500(n)

%o def a(n): return (a263273(2*n + 1) - 1)/2 # _Indranil Ghosh_, May 22 2017

%Y Cf. A263273, A264983.

%Y Cf. also A264989, A264991, A264992.

%K nonn

%O 0,3

%A _Antti Karttunen_, Dec 05 2015