A368431 Distinct values of A367562, in order of appearance and with offset 0.

0, 1, 2, 3, 4, 5, 6, 7, 10, 8, 9, 11, 12, 13, 14, 15, 20, 21, 18, 22, 16, 17, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 42, 40, 41, 43, 44, 36, 37, 45, 34, 38, 46, 32, 33, 35, 39, 47, 50, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 84, 85, 82, 86

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers (with inverse A368432).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms of A367562 and of the present sequence are:
  k   A367562(k)  n   a(n)
  --  ----------  --  ----
   1           0   0     0
   2           1   1     1
   3           2   2     2
   4           0
   5           1
   6           3   3     3
   7           4   4     4
   8           5   5     5
   9           2
  10           6   6     6
  11           0
  12           1
  13           3
  14           7   7     7
  15          10   8    10

Mathematica

With[{imax=7}, DeleteDuplicates[Map[FromDigits[#, 2]&, Flatten[NestList[Map[Delete[{If[Length[#]>1, Map[#<>"0"&, Rest[#]], Nothing], Join[{#[[1]]<>"0"}, Map[#<>"1"&, #]]}, 0]&], {{"0", "1"}}, imax-1]]]]] (* Generates terms up to order 7 *) (* Paolo Xausa, Dec 28 2023 *)

Prog

(PARI) See Links section.
(Python)
from itertools import islice
from functools import reduce
def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])
def agen():  # generator of terms
    R, aset = [["0", "1"]], set()
    while R:
        r = R.pop(0)
        for b in r:
            d = int(b, 2)
            if d not in aset: yield d; aset.add(d)
        if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))
        R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))
print(list(islice(agen(), 70))) # Michael S. Branicky, Dec 24 2023

Crossrefs

Cf. A367508, A367562, A368432 (inverse).

Sequence in context: A082274 A029804 A084690 * A194963 A072794 A181820

Adjacent sequences: A368428 A368429 A368430 * A368432 A368433 A368434

Keyword

nonn,look,base

Author

Rémy Sigrist, Dec 24 2023

Status

approved