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 A300896 #8 Mar 15 2018 15:08:13 %S A300896 1,2,5,3,8,6,4,7,9,16,11,10,12,14,15,13,36,17,19,28,18,20,26,22,21,23, %T A300896 24,25,31,29,68,32,30,66,33,34,61,35,37,56,39,38,51,40,41,47,42,43,44, %U A300896 45,48,52,46,50,49,62,27,55,54,53,57,58,141,59,60,137,63 %N A300896 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n) + a(n+1) + a(n+2) is a Fibbinary number (A003714). %C A300896 This sequence has similarities with A266191: here we consider the sum of triples of consecutive terms, there their product. %C A300896 This sequence is conjectured to be a permutation of the natural numbers. %C A300896 See A300890 for a similar sequence. %H A300896 Rémy Sigrist, <a href="/A300896/b300896.txt">Table of n, a(n) for n = 1..10000</a> %H A300896 Rémy Sigrist, <a href="/A300896/a300896.gp.txt">PARI program for A300896</a> %e A300896 The first terms, alongside the binary representation of triples of consecutive terms, are: %e A300896 n a(n) binary(a(n) + a(n+1) + a(n+2)) %e A300896 -- ---- ------------------------------ %e A300896 1 1 1000 %e A300896 2 2 1010 %e A300896 3 5 10000 %e A300896 4 3 10001 %e A300896 5 8 10010 %e A300896 6 6 10001 %e A300896 7 4 10100 %e A300896 8 7 100000 %e A300896 9 9 100100 %e A300896 10 16 100101 %e A300896 11 11 100001 %e A300896 12 10 100100 %e A300896 13 12 101001 %e A300896 14 14 101010 %e A300896 15 15 1000000 %e A300896 16 13 1000010 %e A300896 17 36 1001000 %e A300896 18 17 1000000 %e A300896 19 19 1000001 %e A300896 20 28 1000010 %o A300896 (PARI) See Links section. %Y A300896 Cf. A003714, A266191, A300890. %K A300896 nonn,base %O A300896 1,2 %A A300896 _Rémy Sigrist_, Mar 14 2018