This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A368427 #20 Dec 28 2023 15:03:56
%S A368427 1,2,3,6,4,5,7,12,13,10,14,8,9,11,15,26,24,25,27,28,20,21,29,18,22,30,
%T A368427 16,17,19,23,31,52,53,50,54,48,49,51,55,56,57,42,58,40,41,43,59,44,60,
%U A368427 36,37,45,61,34,38,46,62,32,33,35,39,47,63,106,104,105
%N A368427 A permutation related to the Christmas tree pattern map (A367508): a(1) = 1, and for any n > 1, a(n) = A053644(n) + A367562(n-1).
%C A368427 This sequence is a permutation of the positive integers (with inverse A368428):
%C A368427 - the Christmas tree pattern map runs through all finite nonempty binary words,
%C A368427 - by prefixing these words with a 1, we obtain the binary expansions of all integers >= 2,
%C A368427 - hence, with the leading term a(1) = 1, we have a permutation of the positive integers.
%C A368427 Apparently, A088163 \ {0} corresponds to the fixed points.
%C A368427 We can also obtain this sequence by applying the Christmas tree pattern map starting from the chain "1" (instead of "0 1") and converting the resulting binary words to decimal.
%H A368427 Rémy Sigrist, <a href="/A368427/b368427.txt">Table of n, a(n) for n = 1..8191</a>
%H A368427 Rémy Sigrist, <a href="/A368427/a368427.gp.txt">PARI program</a>
%H A368427 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A368427 The first terms, alongside their binary expansion and the corresponding word in the Christmas tree pattern map, are:
%e A368427 n a(n) bin(a(n)) Xmas word
%e A368427 -- ---- --------- ---------
%e A368427 1 1 1 N/A
%e A368427 2 2 10 0
%e A368427 3 3 11 1
%e A368427 4 6 110 10
%e A368427 5 4 100 00
%e A368427 6 5 101 01
%e A368427 7 7 111 11
%e A368427 8 12 1100 100
%e A368427 9 13 1101 101
%e A368427 10 10 1010 010
%e A368427 11 14 1110 110
%e A368427 12 8 1000 000
%e A368427 13 9 1001 001
%e A368427 14 11 1011 011
%e A368427 15 15 1111 111
%t A368427 With[{imax=7},Map[FromDigits[#,2]&,Flatten[NestList[Map[Delete[{If[Length[#]>1,Map[#<>"0"&,Rest[#]],Nothing],Join[{#[[1]]<>"0"},Map[#<>"1"&,#]]},0]&],{{"1"}},imax-1]]]] (* Generates terms up to order 7 *) (* _Paolo Xausa_, Dec 28 2023 *)
%o A368427 (PARI) See Links section.
%o A368427 (Python)
%o A368427 from itertools import islice
%o A368427 from functools import reduce
%o A368427 def uniq(r): return reduce(lambda u, e: u if e in u else u+[e], r, [])
%o A368427 def agen(): # generator of terms
%o A368427 R = [["1"]]
%o A368427 while R:
%o A368427 r = R.pop(0)
%o A368427 yield from map(lambda b: int(b, 2), r)
%o A368427 if len(r) > 1: R.append(uniq([r[k]+"0" for k in range(1, len(r))]))
%o A368427 R.append(uniq([r[0]+"0", r[0]+"1"] + [r[k]+"1" for k in range(1, len(r))]))
%o A368427 print(list(islice(agen(), 66))) # _Michael S. Branicky_, Dec 24 2023
%Y A368427 Cf. A053644, A088163, A367508, A367562, A368428 (inverse).
%K A368427 nonn,look,base
%O A368427 1,2
%A A368427 _Rémy Sigrist_, Dec 24 2023