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Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, multiplying n by a(n) does not produce any carries when performed in base 2.
2

%I #7 Jul 10 2017 22:59:28

%S 1,2,4,3,6,5,8,7,10,9,16,17,32,18,33,11,12,14,20,19,24,34,64,21,40,65,

%T 66,36,128,68,129,13,15,22,72,28,48,80,130,25,96,67,256,132,136,257,

%U 258,37,73,133,160,260,512,264,513,137,514,516,520,272,1024,528

%N Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, multiplying n by a(n) does not produce any carries when performed in base 2.

%C This sequence is a self-inverse permutation of the natural numbers.

%C A priori, there are only two fixed points: 1 and 2 (note that a fixed point must be a power of 2).

%C This sequence is related to A266195: here n * a(n), there a(n) * a(n+1), does not produce any carries when performed in base 2.

%H Rémy Sigrist, <a href="/A289726/b289726.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A289726/a289726.gp.txt">PARI program for A289726</a>

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

%e 1 * 1 can be computed without carry in base 2, hence a(1) = 1.

%e 2 * 2 can be computed without carry in base 2, hence a(2) = 2.

%e 3 * 3 cannot be computed without carry in base 2.

%e 3 * 4 can be computed without carry in base 2, hence a(3) = 4.

%o (PARI) See Links section.

%Y Cf. A266195.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Jul 10 2017