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A193360 Concatenation of P{1},P{1,2},P{1,2,3}... where P(A) denotes the power set of A ordered by the size of the subsets, and in each subset, following the increasing order.

%I A193360 #37 Nov 20 2023 11:54:15
%S A193360 1,1,2,1,2,1,2,3,1,2,1,3,2,3,1,2,3,1,2,3,4,1,2,1,3,1,4,2,3,2,4,3,4,1,
%T A193360 2,3,1,2,4,1,3,4,2,3,4,1,2,3,4,1,2,3,4,5,1,2,1,3,1,4,1,5,2,3,2,4,2,5,
%U A193360 3,4,3,5,4,5,1,2,3,1,2,4,1,2,5,1,3,4
%N A193360 Concatenation of P{1},P{1,2},P{1,2,3}... where P(A) denotes the power set of A ordered by the size of the subsets, and in each subset, following the increasing order.
%C A193360 Fractal sequence.
%C A193360 From _Robert Israel_, Jan 09 2023: (Start)
%C A193360 Subsets of the same size are ordered lexicographically.
%C A193360 The first occurrence of k in this sequence is at position (k - 2)*2^(k - 1) + k + 1. (End)
%H A193360 Robert Israel, <a href="/A193360/b193360.txt">Table of n, a(n) for n = 1..10000</a>
%p A193360 comp:= proc(a,b) local i;
%p A193360   for i from 1 do if a[i] < b[i] then return true elif a[i] > b[i] then return false fi od
%p A193360 end proc:
%p A193360 [seq(seq(op(map(op, sort(combinat:-choose(n,k),comp))),k=1..n),n=1..6)]; # _Robert Israel_, Jan 09 2023
%p A193360 # second Maple program:
%p A193360 T:= n-> map(x-> x[], [seq(combinat[choose]([$1..n], i)[], i=1..n)])[]:
%p A193360 seq(T(n), n=1..5);  # _Alois P. Heinz_, Jan 30 2023
%t A193360 t={};Do[t=Join[t,Subsets[Range[n]]],{n,1,5}];Flatten[t]
%t A193360 Table[Subsets[Range[n]],{n,5}]//Flatten (* _Harvey P. Dale_, May 05 2019 *)
%Y A193360 Cf. A082185.
%K A193360 nonn,tabf
%O A193360 1,3
%A A193360 _José María Grau Ribas_, Jul 24 2011