A269838 a(1)=1, then a(n) is the smallest unused multiple of a(A062050(n-1)).

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 12, 16, 15, 18, 27, 24, 11, 14, 21, 20, 25, 30, 36, 32, 28, 40, 48, 64, 45, 54, 81, 72, 13, 22, 33, 44, 35, 42, 63, 56, 49, 50, 60, 80, 75, 90, 108, 96, 55, 70, 84, 100, 125, 120, 144, 128, 112, 160, 192, 256, 135, 162, 243, 216, 17

Offset

1,2

Comments

A permutation of positive integers.

Alternative construction: start with the infinite sequence of all 1s, at step n look up the value of the term at n'th place (k), and if it has been used before, find the smallest unused multiple of k (m*k), find all occurrences of k in the sequence (there are going to be infinitely many), and change every second of them to m*k (see Example).

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

Start with
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
At step 1, do nothing.
At step 2, change every second 1 to 2.
2: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
At step 3, change every other remaining 1 to 3.
3: 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3 2
At step 4, change every other 2 to 4.
4: 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
And so on.
5: 1 2 3 4 5 2 3 4 1 2 3 4 5 2 3 4
6: 1 2 3 4 5 6 3 4 1 2 3 4 5 6 3 4
7: 1 2 3 4 5 6 9 4 1 2 3 4 5 6 9 4
8: 1 2 3 4 5 6 9 8 1 2 3 4 5 6 9 8
9: 1 2 3 4 5 6 9 8 7 2 3 4 5 6 9 8
...

Mathematica

Fold[Append[#1, Min@Complement[Range[Max@#1 + 1]*#1[[#2 - 2^Floor@Log2[#2 - 1]]], #1]] &, {1}, Range[2, 65]] (* Ivan Neretin, Mar 06 2016 *)

Crossrefs

Sequence in context: A068384 A222253 A353591 * A371985 A246376 A269866

Adjacent sequences: A269835 A269836 A269837 * A269839 A269840 A269841

Keyword

nonn

Author

Ivan Neretin, Mar 06 2016

Status

approved