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