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