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

1,3

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

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 *)

Crossrefs

Cf. A082185.

Sequence in context: A136109 A105265 A351468 * A061394 A248141 A220694

Adjacent sequences: A193357 A193358 A193359 * A193361 A193362 A193363

Keyword

nonn,tabf

Author

José María Grau Ribas, Jul 24 2011

Status

approved