cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A163236 Inverse permutation to A163235.

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%I A163236 #19 Jul 03 2025 20:39:48
%S A163236 0,2,1,4,9,5,13,8,6,11,3,7,24,17,18,12,35,27,43,34,14,20,19,26,62,51,
%T A163236 52,42,32,41,25,33,28,37,21,29,58,47,48,38,10,16,15,22,31,23,39,30,
%U A163236 112,97,98,84,70,83,59,71,73,61,85,72,40,50,49,60,135,119,151,134,90
%N A163236 Inverse permutation to A163235.
%H A163236 Antti Karttunen, <a href="/A163236/b163236.txt">Table of n, a(n) for n = 0..4095</a>
%H A163236 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A163236 a(n) = A001477bi(A006068(A059906(n)),A006068(A059905(n))), where A001477bi(x,y) = (((x+y)^2)+x+(3y))/2.
%o A163236 (Scheme) (define (A163236 n) (A001477bi (A006068 (A059906 n)) (A006068 (A059905 n))))
%o A163236 (define (A001477bi x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))
%o A163236 (Python)
%o A163236 def A(x, y): return (((x + y)**2) + x + 3*y)//2
%o A163236 def a006068(n):
%o A163236     s=1
%o A163236     while True:
%o A163236         ns=n>>s
%o A163236         if ns==0: break
%o A163236         n=n^ns
%o A163236         s<<=1
%o A163236     return n
%o A163236 def a059905(n): return sum([(n>>2*i&1)<<i for i in range(int(len(bin(n)[2:])//2) + 1)])
%o A163236 def a059906(n):
%o A163236     x=[int(k) for k in list(bin(n)[2:])][::-1]
%o A163236     return sum([x[2*i + 1]*2**i for i in range(len(x)//2)])
%o A163236 def a(n): return A(a006068(a059906(n)), a006068(a059905(n)))
%o A163236 print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 25 2017
%Y A163236 Inverse: A163235. a(n) = A163234(A057300(n)). Cf. A163234.
%K A163236 nonn
%O A163236 0,2
%A A163236 _Antti Karttunen_, Jul 29 2009