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.
%I A289726 #7 Jul 10 2017 22:59:28 %S A289726 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 A289726 66,36,128,68,129,13,15,22,72,28,48,80,130,25,96,67,256,132,136,257, %U A289726 258,37,73,133,160,260,512,264,513,137,514,516,520,272,1024,528 %N A289726 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 A289726 This sequence is a self-inverse permutation of the natural numbers. %C A289726 A priori, there are only two fixed points: 1 and 2 (note that a fixed point must be a power of 2). %C A289726 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 A289726 Rémy Sigrist, <a href="/A289726/b289726.txt">Table of n, a(n) for n = 1..10000</a> %H A289726 Rémy Sigrist, <a href="/A289726/a289726.gp.txt">PARI program for A289726</a> %H A289726 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %e A289726 1 * 1 can be computed without carry in base 2, hence a(1) = 1. %e A289726 2 * 2 can be computed without carry in base 2, hence a(2) = 2. %e A289726 3 * 3 cannot be computed without carry in base 2. %e A289726 3 * 4 can be computed without carry in base 2, hence a(3) = 4. %o A289726 (PARI) See Links section. %Y A289726 Cf. A266195. %K A289726 nonn,base %O A289726 1,2 %A A289726 _Rémy Sigrist_, Jul 10 2017