A308293 - OEIS

A308293

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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

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

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))).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored scatterplot of (abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1))) for n = 1..32702782 (where the hue is function of n)

Rémy Sigrist, C program for A308293

EXAMPLE

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

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

-- ---- -------------------------------------

1 1 (0,1)

2 2 (1,0)

3 1 (0,0)

4 1 (1,1)