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A362241 Binary encoding of the rows of A362240.

%I A362241 #27 May 08 2023 02:28:26
%S A362241 0,1,0,3,0,5,7,0,10,13,0,3,4,7,14,31,4,9,13,15,17,20,27,28,37,44,51,
%T A362241 53,63,2,15,17,20,28,31,41,44,46,48,53,58,71,78,99,101,123,2,5,7,11,
%U A362241 17,19,24,35,39,41,55,58,63,72,83,85,89,97,107,111,113,134
%N A362241 Binary encoding of the rows of A362240.
%H A362241 Neal Gersh Tolunsky, <a href="/A362241/b362241.txt">Table of n, a(n) for n = 1..10000</a>
%H A362241 Samuel Harkness, <a href="/A362241/a362241.m.txt">MATLAB program</a>
%H A362241 Neal Gersh Tolunsky, <a href="/A362241/a362241.png">Scatterplot of a(n) for n = 1..5196</a>
%F A362241 a(n) = A053645(A362009(n) + 1).
%e A362241 The sequence begins:
%e A362241    n    a(n)     A362240 row
%e A362241   ---   ----     -----------
%e A362241     1     0      0;
%e A362241     2     1      1;
%e A362241     3     0      0, 0;
%e A362241     4     3      1, 1;
%e A362241     5     0      0, 0, 0;
%e A362241     6     5      1, 0, 1;
%e A362241     7     7      1, 1, 1;
%e A362241     8     0      0, 0, 0, 0;
%e A362241     9    10      1, 0, 1, 0;
%e A362241    10    13      1, 1, 0, 1;
%e A362241    11     0      0, 0, 0, 0, 0;
%e A362241    12     3      0, 0, 0, 1, 1;
%e A362241    13     4      0, 0, 1, 0, 0;
%t A362241 V = {0}; K = {0}; B = {0}; While[Length@B < 68, y = 0; While[y == 0, i = Length@V; V[[i]]++; While[V[[i]] == 2 && i > 1 , V[[i]] = 0; i--; V[[i]]++]; If[V[[1]] == 2, V = ConstantArray[0, Length@V + 1]]; z = 0; For[a = 1, a <= Length@K - Length@V + 1, a++, If[K[[a ;; a + Length@V - 1]] == V, z = 1; Break[]]]; If[z == 0, AppendTo[K, V]; b = 0; For[c = Length@V, c > 0, c--, b += V[[c]]*2^(Length@V - c)]; AppendTo[B, b]; K = Flatten[K]; y = 1]]]; Print[B]
%o A362241 (MATLAB) See Links section.
%o A362241 (Python)
%o A362241 from itertools import count, islice, product
%o A362241 def bins(): yield from ("".join(b) for d in count(1) for b in product("01", repeat=d))
%o A362241 def agen(s=""): yield from (int(t, 2) for t in bins() if t not in s and (s:=s+t))
%o A362241 print(list(islice(agen(), 68))) # _Michael S. Branicky_, Apr 12 2023
%Y A362241 Cf. A362240, A053645, A362009, A118248.
%K A362241 nonn,base
%O A362241 1,4
%A A362241 _Samuel Harkness_, Apr 12 2023