A323455 - OEIS

%I #24 Nov 07 2023 19:50:07

%S 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 22,26,28,23,27,29,30,32,33,34,34,36,35,37,38,36,40,37,41,42,38,42,44,

%U 39,43,45,46,40,48,41,49,50,42,50,52,43,51,53,54,44,52,56

%N 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 All the numbers in row n have the same binary weight (A000120) as n.

%H Michael S. Branicky, <a href="/A323455/b323455.txt">Table of n, a(n) for n = 1..10870</a> (Rows 1..2000, flattened)

%e From 7 = 111 we can get 1011 = 11, 1101 = 13, and 1110 = 14, so row 7 is {11,13,14}.

%e The triangle begins:

%e   2,

%e   4,

%e   5, 6,

%e   8,

%e   9, 10,

%e   10, 12,

%e   11, 13, 14,

%e   16,

%e   17, 18,

%e   18, 20,

%e   19, 21, 22,

%e   ...

%t r323455[n_] := Module[{digs=IntegerDigits[n, 2]}, Map[FromDigits[#, 2]&, Map[Insert[digs, 0, #+1]&, Flatten[Position[digs, 1]]]]] (* nth row *)

%t a323455[{m_, n_}] := Flatten[Map[r323455, Range[m, n]]]

%t a323455[{1, 28}] (* _Hartmut F. W. Hoft_, Oct 24 2023 *)

%o (Python)

%o def row(n):

%o     b = bin(n)[2:]

%o     s = set(b[:i+1] + "0" + b[i+1:] for i in range(len(b)) if b[i] == "1")

%o     return sorted(int(w, 2) for w in s)

%o print([c for n in range(1, 29) for c in row(n)]) # _Michael S. Branicky_, Jul 24 2022

%Y Cf. A000120. See A323456 for a closely related sequence, the binary analog of A323386.

%K nonn,base,tabf

%O 1,1

%A _N. J. A. Sloane_, Jan 16 2019

%E More terms from _David Consiglio, Jr._, Jan 17, 2019

%E a(49) and beyond from _Michael S. Branicky_, Jul 24 2022