A231334 Lexicographically earliest sequence of distinct positive integers such that for any distinct i,j, k, the points at positions (i, a(i)), (j, a(j)), (k, a(k)) are not aligned.

1, 2, 4, 3, 6, 5, 9, 12, 7, 14, 13, 8, 23, 17, 18, 22, 10, 15, 11, 28, 19, 16, 20, 29, 32, 44, 35, 39, 24, 40, 26, 37, 42, 21, 56, 64, 43, 31, 25, 34, 27, 33, 66, 67, 52, 60, 30, 57, 36, 63, 86, 82, 38, 50, 47, 69, 75, 79, 89, 49, 45, 76, 41, 48, 98, 77, 94

Offset

1,2

Comments

Is this a permutation of the natural numbers?

There are only two fixed points: 1 and 2.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, C program for this sequence

Illustrations of the first 200 points at positions (n, a(n)) (black pixels correspond to these points, colored pixels (x,y) are aligned with two black pixels (i,a(i)) and (j,a(j))):

(1) x < i < j,

(2) i < x < j,

(3) i < j < x.

Mathematica

WIDTH = 1000;
HEIGHT = 2000;
Clear[seen, aligned, a];
compute[n_] := Module[{c = 1}, While[seen[c] || aligned[n][c], c++; If[c > HEIGHT, Abort[]]]; a[n] = c; seen[a[n]] = True; For[i = 1, i < n, i++, dn = n - i; da = a[n] - a[i]; g = GCD[dn, da]; dn /= g; da /= g; nn = n; na = c; While[True, nn += dn; If[nn > WIDTH, Break[]]; na += da; If[na < 1 || na > HEIGHT, Break[]]; aligned[nn][na] = True]]; a[n]];
Array[compute, WIDTH] (* Jean-François Alcover, Apr 19 2020, translated from Paul Tek's program. *)

Prog

(C) See Link section.

Crossrefs

Cf. A175498, A236266, A236335, A300002.

Sequence in context: A271647 A232643 A366263 * A253609 A300002 A082560

Adjacent sequences: A231331 A231332 A231333 * A231335 A231336 A231337

Keyword

nonn

Author

Paul Tek, Nov 07 2013

Status

approved