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.
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, 22, 26, 28, 23, 27, 29, 30, 32, 33, 34, 34, 36, 35, 37, 38, 36, 40, 37, 41, 42, 38, 42, 44, 39, 43, 45, 46, 40, 48, 41, 49, 50, 42, 50, 52, 43, 51, 53, 54, 44, 52, 56
Offset: 1
Examples
From 7 = 111 we can get 1011 = 11, 1101 = 13, and 1110 = 14, so row 7 is {11,13,14}.
The triangle begins:
2,
4,
5, 6,
8,
9, 10,
10, 12,
11, 13, 14,
16,
17, 18,
18, 20,
19, 21, 22,
...
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10870 (Rows 1..2000, flattened)
Programs
-
Mathematica
r323455[n_] := Module[{digs=IntegerDigits[n, 2]}, Map[FromDigits[#, 2]&, Map[Insert[digs, 0, #+1]&, Flatten[Position[digs, 1]]]]] (* nth row *) a323455[{m_, n_}] := Flatten[Map[r323455, Range[m, n]]] a323455[{1, 28}] (* Hartmut F. W. Hoft, Oct 24 2023 *) -
Python
def row(n): b = bin(n)[2:] s = set(b[:i+1] + "0" + b[i+1:] for i in range(len(b)) if b[i] == "1") return sorted(int(w, 2) for w in s) print([c for n in range(1, 29) for c in row(n)]) # Michael S. Branicky, Jul 24 2022
Extensions
More terms from David Consiglio, Jr., Jan 17 2019
a(49) and beyond from Michael S. Branicky, Jul 24 2022
Comments