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 A330984 #23 Apr 27 2020 08:16:44 %S A330984 0,2,1,5,6,3,4,12,13,14,16,17,7,8,9,34,10,11,30,31,32,35,36,33,37,41, %T A330984 42,43,45,46,18,19,20,23,15,21,22,24,88,89,92,25,26,27,81,28,29,77,78, %U A330984 79,82,83,80,84,90,93,91,94,106,85,86,95,96,87,97,107,108 %N A330984 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n and a(n) have no common 1 in their base phi representations. %C A330984 This sequence is a self-inverse permutation of the nonnegative integers. %H A330984 Rémy Sigrist, <a href="/A330984/b330984.txt">Table of n, a(n) for n = 0..10000</a> %H A330984 Rémy Sigrist, <a href="/A330984/a330984.png">Scatterplot of (x, y) such that x and y have no common 1 in their base phi representations and 0 <= x, y <= 1000</a> %H A330984 Rémy Sigrist, <a href="/A330984/a330984.gp.txt">PARI program for A330984</a> %H A330984 Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a> %H A330984 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %e A330984 The first terms, alongside the base phi representations of n and of a(n), are: %e A330984 n a(n) phi(n) phi(a(n)) %e A330984 -- ---- ---------- ------------- %e A330984 0 0 0 0 %e A330984 1 2 1 10.01 %e A330984 2 1 10.01 1 %e A330984 3 5 100.01 1000.1001 %e A330984 4 6 101.01 1010.0001 %e A330984 5 3 1000.1001 100.01 %e A330984 6 4 1010.0001 101.01 %e A330984 7 12 10000.0001 100000.101001 %e A330984 8 13 10001.0001 100010.001001 %e A330984 9 14 10010.0101 100100.001001 %e A330984 10 16 10100.0101 101000.100001 %o A330984 (PARI) See Links section. %Y A330984 Cf. A238757 (binary analog), A331212. %K A330984 nonn,base %O A330984 0,2 %A A330984 _Rémy Sigrist_, Apr 23 2020