The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A308293

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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.
(history; published version)

#13 by Sean A. Irvine at Thu May 23 01:37:11 EDT 2019

STATUS

proposed

approved

#12 by Rémy Sigrist at Mon May 20 00:13:55 EDT 2019

STATUS

editing

proposed

Discussion

Mon May 20

01:03

Luca Petrone: Shouldn't a lexicographically earliest sequence be without repetition of terms?

11:57

Rémy Sigrist: Luca: lexicographical ordering applies to sequences in general, without restriction on whether or not they have distinct terms. here we accept duplicates in the sequence, but not in the associate sequence (b(n)) = ((abs(a(n+2)-a(n)), abs(a(n+2)-a(n+1)))).

#11 by Rémy Sigrist at Mon May 20 00:13:25 EDT 2019

LINKS

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

STATUS

approved

editing

Discussion

Mon May 20

00:13

Rémy Sigrist: added b-file

#10 by Susanna Cuyler at Sun May 19 20:41:20 EDT 2019

STATUS

proposed

approved

#9 by Rémy Sigrist at Sun May 19 11:13:26 EDT 2019

STATUS

editing

proposed

#8 by Rémy Sigrist at Sun May 19 03:59:53 EDT 2019

CROSSREFS

See A080427 for a simpler variant.

Cf. A080427, A157128.

#7 by Rémy Sigrist at Sun May 19 03:56:59 EDT 2019

CROSSREFS

Cf. A080427, A157128.

#6 by Rémy Sigrist at Sun May 19 03:04:59 EDT 2019

COMMENTS

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

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

#5 by Rémy Sigrist at Sun May 19 03:03:09 EDT 2019

COMMENTS

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

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))).

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)

CROSSREFS

Cf. A157128.

#4 by Rémy Sigrist at Sun May 19 02:53:02 EDT 2019

LINKS

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)

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

PROG

(C) See Links section.