A352778 Numbers k such that w(k + w(k)) > w(k), where w(k) is the binary weight of k, A000120(k).

2, 4, 5, 8, 9, 12, 16, 17, 20, 24, 26, 27, 28, 32, 33, 36, 40, 42, 43, 44, 48, 50, 51, 52, 56, 57, 58, 64, 65, 68, 72, 74, 75, 76, 80, 82, 83, 84, 88, 89, 90, 96, 98, 99, 100, 104, 105, 106, 112, 113, 114, 118, 120, 121, 122, 128, 129, 132, 136, 138, 139, 140, 144, 146, 147, 148, 152, 153, 154, 160, 162, 163, 164

Offset: 1

Author

Ctibor O. Zizka, Apr 02 2022

Keywords

• nonn
• base
• easy

Examples

			k = 17; A000120(17 + A000120(17)) > A000120(17), thus k = 17 is a term.
		

Crossrefs

Cf. A000120, A092391, A348367.

Programs

Mathematica

w[n_] := DigitCount[n, 2, 1]; Select[Range[200], 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(165) if ok(k)]) # Michael S. Branicky, Apr 02 2022

Formula

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