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A323455 Irregular triangle read by rows: row n lists the numbers that can be obtained from the binary expansion of n by inserting a single 0 after any 1.

%I A323455 #26 Jun 27 2025 22:39:13
%S A323455 2,4,5,6,8,9,10,10,12,11,13,14,16,17,18,18,20,19,21,22,20,24,21,25,26,
%T A323455 22,26,28,23,27,29,30,32,33,34,34,36,35,37,38,36,40,37,41,42,38,42,44,
%U A323455 39,43,45,46,40,48,41,49,50,42,50,52,43,51,53,54,44,52,56
%N A323455 Irregular triangle read by rows: row n lists the numbers that can be obtained from the binary expansion of n by inserting a single 0 after any 1.
%C A323455 All the numbers in row n have the same binary weight (A000120) as n.
%H A323455 Michael S. Branicky, <a href="/A323455/b323455.txt">Table of n, a(n) for n = 1..10870</a> (Rows 1..2000, flattened)
%e A323455 From 7 = 111 we can get 1011 = 11, 1101 = 13, and 1110 = 14, so row 7 is {11,13,14}.
%e A323455 The triangle begins:
%e A323455   2,
%e A323455   4,
%e A323455   5, 6,
%e A323455   8,
%e A323455   9, 10,
%e A323455   10, 12,
%e A323455   11, 13, 14,
%e A323455   16,
%e A323455   17, 18,
%e A323455   18, 20,
%e A323455   19, 21, 22,
%e A323455   ...
%t A323455 r323455[n_] := Module[{digs=IntegerDigits[n, 2]}, Map[FromDigits[#, 2]&, Map[Insert[digs, 0, #+1]&, Flatten[Position[digs, 1]]]]] (* nth row *)
%t A323455 a323455[{m_, n_}] := Flatten[Map[r323455, Range[m, n]]]
%t A323455 a323455[{1, 28}] (* _Hartmut F. W. Hoft_, Oct 24 2023 *)
%o A323455 (Python)
%o A323455 def row(n):
%o A323455     b = bin(n)[2:]
%o A323455     s = set(b[:i+1] + "0" + b[i+1:] for i in range(len(b)) if b[i] == "1")
%o A323455     return sorted(int(w, 2) for w in s)
%o A323455 print([c for n in range(1, 29) for c in row(n)]) # _Michael S. Branicky_, Jul 24 2022
%Y A323455 Cf. A000120. See A323456 for a closely related sequence, the binary analog of A323386.
%K A323455 nonn,base,tabf
%O A323455 1,1
%A A323455 _N. J. A. Sloane_, Jan 16 2019
%E A323455 More terms from _David Consiglio, Jr._, Jan 17 2019
%E A323455 a(49) and beyond from _Michael S. Branicky_, Jul 24 2022