A342101 Remove middle term and append, starting with [1, 2, 3].

1, 2, 3, 1, 3, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 3, 1, 2, 3, 1, 3, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 3, 1, 2, 3, 1, 3, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 1, 3, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 3, 1, 2, 3, 1, 3, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 3, 1, 2, 3, 1, 3

Offset: 1

Author

Matthew Malone, Feb 28 2021

Keywords

• nonn

Examples

			Start with [1, 2, 3], take that sequence, remove the middle term, 2, and append to the original sequence, yielding [1, 2, 3, 1, 3]. Then repeat this process to give [1, 2, 3, 1, 3, 1, 2, 1, 3], and so on.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..65537
• Kevin Ryde, PARI/GP Code and Notes.

Crossrefs

Cf. A000051.

Programs

Kotlin

fun A342101(iter: Int): List = removeMiddle(listOf(1,2,3), iter)
fun removeMiddle(initial: List, iter: Int): List {
  if (iter < 2) return initial
  val prev = removeMiddle(initial, iter-1)
  return prev + prev.subList(0, (prev.size - 1) / 2) + prev.subList((prev.size + 1) /2, prev.size)
}

Maple

T:= proc(n) option remember; `if`(n=1, [$1..3][],
      subsop(2^(n-2)+1=[][], [seq(T(i), i=1..n-1)])[])
    end:
seq(T(n), n=1..8);  # Alois P. Heinz, Apr 12 2021

Mathematica

Nest[Join[#, Drop[#, {(Length[#] + 1)/2}]] &, Range[3], 6] (* Michael De Vlieger, May 01 2021 *)

PARI

first(n) = { my(v = [1,2,3]); for(i = 1, logint(n-1, 2), cv = v[^(#v + 1)\2]; v = concat(v, cv) ); v } \\ David A. Corneth, Apr 14 2021

PARI

\\ Also see links.

Python

def aupton(terms):
  alst = [1, 2, 3]
  while len(alst) < terms:
    alst += alst[:len(alst)//2] + alst[(len(alst)+1)//2:]
  return alst[:terms]
print(aupton(87)) # Michael S. Branicky, Mar 26 2021