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

Author

Rémy Sigrist, Dec 24 2023

Keywords

• nonn
• look
• base

Comments

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

Examples

			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
		

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

Crossrefs

Cf. A367508, A367562, A368432 (inverse).

Programs

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 *)

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