cp's OEIS Frontend

A163234 Inverse permutation to A163233.

%I A163234 #20 Jul 04 2025 12:36:51
%S A163234 0,1,2,4,6,3,11,7,9,13,5,8,24,18,17,12,28,21,37,29,10,15,16,22,58,48,
%T A163234 47,38,31,39,23,30,35,43,27,34,62,52,51,42,14,19,20,26,32,25,41,33,
%U A163234 112,98,97,84,73,85,61,72,70,59,83,71,40,49,50,60,120,105,137,121,78
%N A163234 Inverse permutation to A163233.
%H A163234 Antti Karttunen, <a href="/A163234/b163234.txt">Table of n, a(n) for n = 0..4095</a>
%H A163234 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A163234 a(n) = A001477bi(A006068(A059905(n)),A006068(A059906(n))), where A001477bi(x,y) = (((x+y)^2)+x+(3y))/2.
%o A163234 (Scheme) (define (A163234 n) (A001477bi (A006068 (A059905 n)) (A006068 (A059906 n))))
%o A163234 (define (A001477bi x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
%o A163234 (Python)
%o A163234 def A(x, y): return (((x + y)**2) + x + 3*y)//2
%o A163234 def a006068(n):
%o A163234     s=1
%o A163234     while True:
%o A163234         ns=n>>s
%o A163234         if ns==0: break
%o A163234         n=n^ns
%o A163234         s<<=1
%o A163234     return n
%o A163234 def a059905(n): return sum([(n>>2*i&1)<<i for i in range(int(len(bin(n)[2:])//2) + 1)])
%o A163234 def a059906(n):
%o A163234     x=[int(k) for k in list(bin(n)[2:])][::-1]
%o A163234     return sum([x[2*i + 1]*2**i for i in range(len(x)//2)])
%o A163234 def a(n): return A(a006068(a059905(n)), a006068(a059906(n)))
%o A163234 print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 25 2017
%Y A163234 Inverse: A163233. a(n) = A163236(A057300(n)). Cf. A163236.
%K A163234 nonn
%O A163234 0,3
%A A163234 _Antti Karttunen_, Jul 29 2009