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

1,1

Comments

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

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10870 (Rows 1..2000, flattened)

Example

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,
  ...

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A230581 A361825 A248962 * A133398 A138836 A175431

Adjacent sequences: A323452 A323453 A323454 * A323456 A323457 A323458

Keyword

nonn,base,tabf

Author

N. J. A. Sloane, Jan 16 2019

Extensions

More terms from David Consiglio, Jr., Jan 17, 2019

a(49) and beyond from Michael S. Branicky, Jul 24 2022

Status

approved