OFFSET
1,2
COMMENTS
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.
The sequence is a permutation of the natural numbers.
LINKS
EXAMPLE
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:
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,...
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini, Aug 02 2016
STATUS
approved