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

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, 20, 40, 21, 42, 23, 46, 25, 50, 27, 54, 28, 56, 29, 58, 31, 62, 33, 66, 35, 70, 36, 72, 37, 74, 39, 78, 41, 82, 43, 86, 44, 88, 45, 90, 47, 94, 48, 96, 49, 98, 51, 102

Offset

1,2

Comments

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

P. Erdős, R. Freud, and N. Hegyvári, Arithmetical properties of permutations of integers, Acta Mathematica Hungarica 41:1-2 (1983), pp. 169-176.

Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625[math.CO], 2020-2021.

Index entries for sequences that are permutations of the natural numbers

Mathematica

w = {}; Do[ w = If[ FreeQ[w, k], w = Join[w, {k, 2k}], w], {k, 100}]; w
(* Jean-François Alcover, Nov 04 2011, after Wouter Meeussen *)

Prog

(Haskell)
import Data.List (delete)
a036552 n = a036552_list !! (n-1)
a036552_list = g [1..] where
   g (x:xs) = x : (2*x) : (g $ delete (2*x) xs)
-- Reinhard Zumkeller, Feb 07 2011
(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

Crossrefs

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

Sequence in context: A154285 A362484 A258078 * A257987 A372132 A132169

Adjacent sequences: A036549 A036550 A036551 * A036553 A036554 A036555

Keyword

nonn,easy,nice

Author

Tom Verhoeff

Status

approved