cp's OEIS Frontend

A036552 List of pairs (m,2m) where m is the least unused positive number.

%I A036552 #45 May 09 2024 10:33:34
%S A036552 1,2,3,6,4,8,5,10,7,14,9,18,11,22,12,24,13,26,15,30,16,32,17,34,19,38,
%T A036552 20,40,21,42,23,46,25,50,27,54,28,56,29,58,31,62,33,66,35,70,36,72,37,
%U A036552 74,39,78,41,82,43,86,44,88,45,90,47,94,48,96,49,98,51,102
%N A036552 List of pairs (m,2m) where m is the least unused positive number.
%C A036552 A permutation of the natural numbers. Inverse permutation is A065037.
%H A036552 Reinhard Zumkeller, <a href="/A036552/b036552.txt">Table of n, a(n) for n = 1..10000</a>
%H A036552 P. Erdős, R. Freud, and N. Hegyvári, <a href="https://users.renyi.hu/~p_erdos/1983-02.pdf">Arithmetical properties of permutations of integers</a>, Acta Mathematica Hungarica 41:1-2 (1983), pp. 169-176.
%H A036552 Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, <a href="https://arxiv.org/abs/2012.04625">Finding structure in sequences of real numbers via graph theory: a problem list</a>, arXiv:2012.04625[math.CO], 2020-2021.
%H A036552 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t A036552 w = {}; Do[ w = If[ FreeQ[w, k], w = Join[w, {k, 2k}], w], {k, 100}]; w
%t A036552 (* _Jean-François Alcover_, Nov 04 2011, after _Wouter Meeussen_ *)
%o A036552 (Haskell)
%o A036552 import Data.List (delete)
%o A036552 a036552 n = a036552_list !! (n-1)
%o A036552 a036552_list = g [1..] where
%o A036552    g (x:xs) = x : (2*x) : (g $ delete (2*x) xs)
%o A036552 -- _Reinhard Zumkeller_, Feb 07 2011
%o A036552 (PARI) apairs(N) = my(m=0, r=List(), i=0); while(#r<N*2, if(!bitand(m, 1<<(i++)), listput(~r, i); listput(~r, i*2); m=bitor(m, 1<<(i*2)))); Vec(r); \\ _Ruud H.G. van Tol_, May 09 2024
%Y A036552 Alternating merge of A003159 and A036554. Cf. A064736, A065037.
%K A036552 nonn,easy,nice
%O A036552 1,2
%A A036552 _Tom Verhoeff_