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

1,3

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.

Links

Table of n, a(n) for n=1..69.

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000120, A092391, A348367.

Sequence in context: A169939 A357627 A073108 * A255160 A344892 A357555

Adjacent sequences: A352773 A352774 A352775 * A352777 A352778 A352779

Keyword

nonn,base,easy

Author

Ctibor O. Zizka, Apr 02 2022

Status

approved