|
%I #16 Mar 18 2022 21:52:34
%S 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 47,38,31,39,23,30,35,43,27,34,62,52,51,42,14,19,20,26,32,25,41,33,
%U 112,98,97,84,73,85,61,72,70,59,83,71,40,49,50,60,120,105,137,121,78
%N Inverse permutation to A163233.
%H Antti Karttunen, <a href="/A163234/b163234.txt">Table of n, a(n) for n = 0..4095</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) = A001477bi(A006068(A059905(n)),A006068(A059906(n))), where A001477bi(x,y) = (((x+y)^2)+x+(3y))/2.
%o (Scheme:) (define (A163234 n) (A001477bi (A006068 (A059905 n)) (A006068 (A059906 n))))
%o (define (A001477bi x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
%o (Python)
%o def A(x, y): return (((x + y)**2) + x + 3*y)//2
%o def a006068(n):
%o s=1
%o while True:
%o ns=n>>s
%o if ns==0: break
%o n=n^ns
%o s<<=1
%o return n
%o def a059905(n): return sum([(n>>2*i&1)<<i for i in range(int(len(bin(n)[2:])//2) + 1)])
%o def a059906(n):
%o x=[int(k) for k in list(bin(n)[2:])][::-1]
%o return sum([x[2*i + 1]*2**i for i in range(len(x)//2)])
%o def a(n): return A(a006068(a059905(n)), a006068(a059906(n)))
%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 25 2017
%Y Inverse: A163233. a(n) = A163236(A057300(n)). Cf. A163236.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jul 29 2009
|
