A269838 - OEIS

%I #6 Mar 29 2016 06:05:02

%S 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,

%T 48,64,45,54,81,72,13,22,33,44,35,42,63,56,49,50,60,80,75,90,108,96,

%U 55,70,84,100,125,120,144,128,112,160,192,256,135,162,243,216,17

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

%C A permutation of positive integers.

%C 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).

%H Ivan Neretin, <a href="/A269838/b269838.txt">Table of n, a(n) for n = 1..10000</a>

%e Start with

%e 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

%e At step 1, do nothing.

%e At step 2, change every second 1 to 2.

%e 2: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

%e At step 3, change every other remaining 1 to 3.

%e 3: 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3 2

%e At step 4, change every other 2 to 4.

%e 4: 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

%e And so on.

%e 5: 1 2 3 4 5 2 3 4 1 2 3 4 5 2 3 4

%e 6: 1 2 3 4 5 6 3 4 1 2 3 4 5 6 3 4

%e 7: 1 2 3 4 5 6 9 4 1 2 3 4 5 6 9 4

%e 8: 1 2 3 4 5 6 9 8 1 2 3 4 5 6 9 8

%e 9: 1 2 3 4 5 6 9 8 7 2 3 4 5 6 9 8

%e ...

%t 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 *)

%K nonn

%O 1,2

%A _Ivan Neretin_, Mar 06 2016