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.

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, 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, 3, 4, 3, 5, 4, 5, 1, 2, 3, 1, 2, 4, 1, 2, 5, 1, 3, 4

Offset: 1

Author

José María Grau Ribas, Jul 24 2011

Keywords

• nonn
• tabf

Comments

Fractal sequence.

From Robert Israel, Jan 09 2023: (Start)

Subsets of the same size are ordered lexicographically.

The first occurrence of k in this sequence is at position (k - 2)*2^(k - 1) + k + 1. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A082185.

Programs

Maple

comp:= proc(a,b) local i;
  for i from 1 do if a[i] < b[i] then return true elif a[i] > b[i] then return false fi od
end proc:
[seq(seq(op(map(op, sort(combinat:-choose(n,k),comp))),k=1..n),n=1..6)]; # Robert Israel, Jan 09 2023
# second Maple program:
T:= n-> map(x-> x[], [seq(combinat[choose]([$1..n], i)[], i=1..n)])[]:
seq(T(n), n=1..5);  # Alois P. Heinz, Jan 30 2023

Mathematica

t={};Do[t=Join[t,Subsets[Range[n]]],{n,1,5}];Flatten[t]
Table[Subsets[Range[n]],{n,5}]//Flatten (* Harvey P. Dale, May 05 2019 *)