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

%I A368431 #21 Dec 28 2023 15:04:08
%S A368431 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,
%T A368431 26,27,28,29,30,31,42,40,41,43,44,36,37,45,34,38,46,32,33,35,39,47,50,
%U A368431 48,49,51,52,53,54,55,56,57,58,59,60,61,62,63,84,85,82,86
%N A368431 Distinct values of A367562, in order of appearance and with offset 0.
%C A368431 This sequence is a permutation of the nonnegative integers (with inverse A368432).
%H A368431 Rémy Sigrist, <a href="/A368431/b368431.txt">Table of n, a(n) for n = 0..8191</a>
%H A368431 Rémy Sigrist, <a href="/A368431/a368431.gp.txt">PARI program</a>
%H A368431 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A368431 The first terms of A367562 and of the present sequence are:
%e A368431   k   A367562(k)  n   a(n)
%e A368431   --  ----------  --  ----
%e A368431    1           0   0     0
%e A368431    2           1   1     1
%e A368431    3           2   2     2
%e A368431    4           0
%e A368431    5           1
%e A368431    6           3   3     3
%e A368431    7           4   4     4
%e A368431    8           5   5     5
%e A368431    9           2
%e A368431   10           6   6     6
%e A368431   11           0
%e A368431   12           1
%e A368431   13           3
%e A368431   14           7   7     7
%e A368431   15          10   8    10
%t A368431 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 *)
%o A368431 (PARI) See Links section.
%o A368431 (Python)
%o A368431 from itertools import islice
%o A368431 from functools import reduce
%o A368431 def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])
%o A368431 def agen():  # generator of terms
%o A368431     R, aset = [["0", "1"]], set()
%o A368431     while R:
%o A368431         r = R.pop(0)
%o A368431         for b in r:
%o A368431             d = int(b, 2)
%o A368431             if d not in aset: yield d; aset.add(d)
%o A368431         if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))
%o A368431         R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))
%o A368431 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Dec 24 2023
%Y A368431 Cf. A367508, A367562, A368432 (inverse).
%K A368431 nonn,look,base
%O A368431 0,3
%A A368431 _Rémy Sigrist_, Dec 24 2023