A265351 - OEIS

%I #11 May 25 2017 03:17:14

%S 0,1,2,3,4,11,6,5,8,9,10,29,12,13,38,33,32,35,18,7,20,15,14,17,24,23,

%T 26,27,28,83,30,31,92,87,86,89,36,37,110,39,40,119,114,113,116,99,34,

%U 101,96,95,98,105,104,107,54,19,56,21,22,65,60,59,62,45,16,47,42,41,44,51,50,53,72,25,74,69,68,71,78,77,80,81

%N Permutation of nonnegative integers: a(n) = A263272(A263273(n)).

%C Composition of A263273 with the permutation obtained from its even bisection.

%H Antti Karttunen, <a href="/A265351/b265351.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) = A263272(A263273(n)).

%F As a composition of other related permutations:

%F a(n) = A264974(A265367(n)).

%F Other identities. For all n >= 0:

%F a(3*n) = 3*a(n).

%F a(n) = A265342(n)/2.

%o (Scheme) (define (A265351 n) (A263272 (A263273 n)))

%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 a263272(n): return a263273(2*n)/2

%o def a(n): return a263272(a263273(n)) # _Indranil Ghosh_, May 25 2017

%Y Inverse: A265352.

%Y Cf. A263272, A263273, A264974, A265367.

%Y Cf. also A265342, A265353, A265355, A265356.

%K nonn,base

%O 0,3

%A _Antti Karttunen_, Dec 07 2015