A229830 Trajectory of 1 under the morphism 1 -> 12, 2 -> 1232, 3 -> 123432, 4 -> 12345432, etc.

1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1

Offset: 1

Author

Franklin T. Adams-Watters, Dec 08 2013

Keywords

• nonn

Comments

It appears that records occur at A000111. [This is false. - Rémy Sigrist, Nov 15 2018]

The n-th local maximum equals a(n) + 1. - Rémy Sigrist, Nov 13 2018

Records at {1, 2, 5, 16, 61, 258, 1161, 5440, 26233, 129282, 648141, 3294864, ...}, which seems to match A104858. - Michael De Vlieger, Nov 13 2018

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8558 (7 iterations)
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A007001, A000111.

Programs

Mathematica

With[{n = 5}, Take[#, LengthWhile[#, # <= n &] + 1] &@ Nest[Flatten[# /. Array[Last@ # - 1 -> Most[#~Join~Reverse@ Most@ #] &@ Range@ # &, Max@ #, 2]] &, {1}, n]] (* Michael De Vlieger, Nov 13 2018 *)

PARI

my(a = vector(87), n=0); a[1]=1; for (p=1, oo, my(h=1+a[p]); for (v=1, h, a[n++]=v; print1 (v ", "); if (n==#a, break (2))); forstep (v=h-1, 2, -1, a[n++]=v; print1 (v ", "); if (n==#a, break (2)))) \\ Rémy Sigrist, Nov 13 2018

Extensions

Data corrected by Rémy Sigrist, Nov 13 2018