A352776 Numbers k such that w(k + w(k)) = w(k), where w(k) is the binary weight of k, A000120(k).

0, 1, 3, 10, 11, 18, 19, 22, 23, 25, 34, 35, 38, 39, 41, 49, 53, 54, 66, 67, 70, 71, 73, 81, 85, 86, 97, 101, 102, 110, 116, 117, 119, 130, 131, 134, 135, 137, 145, 149, 150, 161, 165, 166, 174, 180, 181, 183, 193, 197, 198, 206, 212, 213, 215, 228, 229, 231, 236, 237, 243, 246, 247, 258, 259, 262, 263, 265, 273

Offset: 1

Author

Ctibor O. Zizka, Apr 02 2022

Keywords

• nonn
• base
• easy

Comments

w(k + w(k)) - w(k) = 0 this sequence, w(k + w(k)) - w(k) = 2 for k = 4*j, where A000120(j) = 3.

Examples

			k = 18; A000120(18 + A000120(18)) = A000120(18), thus k = 18 is a term.
		

Crossrefs

Cf. A000120, A092391, A348367.

Programs

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(274) if ok(k)]) # Michael S. Branicky, Apr 02 2022

Formula

k : A000120(A092391(k)) = A000120(k); A348367(k) = A000120(k).