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

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)
   5     1  (2,1)
   6     2  (1,2)
   7     3  (2,0)
   8     1  (2,2)
   9     1  (0,2)
  10     3  (1,3)
  11     1  (0,3)
  12     4  (3,0)
  13     1  (3,3)
  14     1  (4,1)
  15     4  (3,4)

Prog

(C) See Links section.

Crossrefs

See A080427 for a simpler variant.

Cf. A157128.

Sequence in context: A331958 A319193 A097886 * A249298 A088863 A053283

Adjacent sequences: A308290 A308291 A308292 * A308294 A308295 A308296

Keyword

nonn

Author

Rémy Sigrist, May 19 2019

Status

approved