A352785 Numbers k such that w(k - w(k)) = w(k), where w(k) is the binary weight of k, A000120(k).

0, 2, 5, 12, 14, 20, 22, 25, 27, 28, 36, 38, 41, 43, 44, 52, 57, 58, 68, 70, 73, 75, 76, 84, 89, 90, 100, 105, 106, 115, 120, 122, 125, 132, 134, 137, 139, 140, 148, 153, 154, 164, 169, 170, 179, 184, 186, 189, 196, 201, 202, 211, 216, 218, 221, 232, 234, 237, 241, 243, 249, 252, 254, 260, 262, 265, 267, 268, 276

Offset: 1

Author

Ctibor O. Zizka, Apr 02 2022

Keywords

• nonn
• base
• easy

Examples

			k = 20; A000120(20 - A000120(20)) = A000120(20), thus k = 20 is a term.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A011371, A352784.

Programs

Maple

q:= n-> (w-> w(n-w(n))=w(n))(k-> add(i, i=Bits[Split](k))):
select(q, [$0..300])[];  # Alois P. Heinz, May 24 2022

Mathematica

w[n_] := DigitCount[n, 2, 1]; Select[Range[0, 300], w[# - w[#]] == w[#] &] (* Amiram Eldar, Apr 02 2022 *)

Python

def w(n): return bin(n).count("1")
def ok(n): wn = w(n); return w(n - wn) == wn
print([k for k in range(277) if ok(k)]) # Michael S. Branicky, Apr 02 2022

Formula

k : A000120(A011371(k)) = A000120(k); A352784(k) = A000120(k).