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A036552 List of pairs (m,2m) where m is the least unused positive number. 6

%I #41 Jan 13 2024 10:44:24

%S 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 20,40,21,42,23,46,25,50,27,54,28,56,29,58,31,62,33,66,35,70,36,72,37,

%U 74,39,78,41,82,43,86,44,88,45,90,47,94,48,96,49,98,51,102

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

%C A permutation of the natural numbers. Inverse permutation is A065037.

%H Reinhard Zumkeller, <a href="/A036552/b036552.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 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 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%t w = {}; Do[ w = If[ FreeQ[w, k], w = Join[w, {k, 2k}], w], {k, 100}]; w

%t (* _Jean-François Alcover_, Nov 04 2011, after _Wouter Meeussen_ *)

%o (Haskell)

%o import Data.List (delete)

%o a036552 n = a036552_list !! (n-1)

%o a036552_list = g [1..] where

%o g (x:xs) = x : (2*x) : (g $ delete (2*x) xs)

%o -- _Reinhard Zumkeller_, Feb 07 2011

%Y Alternating merge of A003159 and A036554. Cf. A064736, A065037.

%K nonn,easy,nice

%O 1,2

%A _Tom Verhoeff_

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)