A300896 - OEIS

%I #8 Mar 15 2018 15:08:13

%S 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 24,25,31,29,68,32,30,66,33,34,61,35,37,56,39,38,51,40,41,47,42,43,44,

%U 45,48,52,46,50,49,62,27,55,54,53,57,58,141,59,60,137,63

%N 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 This sequence has similarities with A266191: here we consider the sum of triples of consecutive terms, there their product.

%C This sequence is conjectured to be a permutation of the natural numbers.

%C See A300890 for a similar sequence.

%H Rémy Sigrist, <a href="/A300896/b300896.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A300896/a300896.gp.txt">PARI program for A300896</a>

%e The first terms, alongside the binary representation of triples of consecutive terms, are:

%e   n   a(n)    binary(a(n) + a(n+1) + a(n+2))

%e   --  ----    ------------------------------

%e    1     1       1000

%e    2     2       1010

%e    3     5      10000

%e    4     3      10001

%e    5     8      10010

%e    6     6      10001

%e    7     4      10100

%e    8     7     100000

%e    9     9     100100

%e   10    16     100101

%e   11    11     100001

%e   12    10     100100

%e   13    12     101001

%e   14    14     101010

%e   15    15    1000000

%e   16    13    1000010

%e   17    36    1001000

%e   18    17    1000000

%e   19    19    1000001

%e   20    28    1000010

%o (PARI) See Links section.

%Y Cf. A003714, A266191, A300890.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Mar 14 2018