A308293 - OEIS

%I #13 May 23 2019 01:37:11

%S 1,2,1,1,1,2,3,1,1,3,1,4,1,1,4,5,1,1,5,1,2,4,6,1,1,6,1,4,6,2,1,6,2,7,

%T 1,1,7,1,8,1,1,8,3,1,7,8,1,2,5,8,1,9,1,1,9,3,1,8,9,1,3,6,10,1,1,10,1,

%U 5,8,2,10,1,8,10,1,11,1,1,11,4,1,9,10,1

%N Lexicographically earliest sequence of positive terms such that a(1) = 1, a(2) = 2, and for any n > 0, (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))) is unique.

%C This sequence shows chaotic behavior (see scatterplot in Links section).

%C This behavior is determined by the choice of the two leading terms.

%C The variant, say b, with b(1) = b(2) = 1, corresponds to the natural numbers interspersed with pairs of ones: 1,1,1, 2,1,1, 3,1,1, etc. (b(n) = abs(A157128(n))).

%H Rémy Sigrist, <a href="/A308293/b308293.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A308293/a308293.png">Colored scatterplot of (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))) for n = 1..32702782</a> (where the hue is function of n)

%H Rémy Sigrist, <a href="/A308293/a308293.txt">C program for A308293</a>

%e The first terms, alongside (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))), are:

%e   n   a(n)  (abs(a(n+2)-a(n)),abs(a(n+2)-a(n+1)))

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

%e    1     1  (0,1)

%e    2     2  (1,0)

%e    3     1  (0,0)

%e    4     1  (1,1)

%e    5     1  (2,1)

%e    6     2  (1,2)

%e    7     3  (2,0)

%e    8     1  (2,2)

%e    9     1  (0,2)

%e   10     3  (1,3)

%e   11     1  (0,3)

%e   12     4  (3,0)

%e   13     1  (3,3)

%e   14     1  (4,1)

%e   15     4  (3,4)

%o (C) See Links section.

%Y See A080427 for a simpler variant.

%Y Cf. A157128.

%K nonn

%O 1,2

%A _Rémy Sigrist_, May 19 2019