A275583 - OEIS

%I #14 May 13 2022 14:04:42

%S 1,2,3,4,5,6,9,7,8,10,11,12,15,18,13,14,16,17,19,20,21,24,27,30,22,23,

%T 25,26,28,29,31,32,33,36,39,42,45,34,35,37,38,40,41,43,44,46,47,48,51,

%U 54,57,60,63,49,50,52,53,55,56,58,59,61,62,64,65,66,69,72,75,78,81,84,87,90,67,68,70,71,73,74,76,77,79,80,82,83,85,86,88,89,91,92,93

%N The multiples of 3 of the sequence appear in blocks. The successive sizes of these blocks are given by the sequence itself.

%C The sequence is started with a(1)=1 and always extended with the smallest integer not yet used that doesn't lead to a contradiction.

%C The sequence is a permutation of the natural numbers.

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The blocks of multiples of 3 are indicated here by parentheses; the successive block-sizes are 1, 2, 3, 4, 5, ... which reproduces the sequence itself:

%e 1,2,(3),4,5,(6,9),7,8,10,11,(12,15,18),13,14,16,17,19,20,(21,24,27,30),22,23,25,26,28,29,31,32,(33,36,39,42,45),34,...

%t a[1]=1;a[n_]:=a[n]=Block[{k=1},While[MemberQ[s=Array[a,n-1],k]||(g=Length/@Select[SplitBy[Join[s,{k}],Mod[#,3]==0&],Mod[First@#,3]==0&];g!=s[[;;Length@g]]),If[Mod[k,3]==0&&FreeQ[s,k],Break[],k++]];k];Array[a,93] (* _Giorgos Kalogeropoulos_, May 12 2022 *)

%K nonn,base

%O 1,2

%A _Eric Angelini_, Aug 02 2016