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A352776
Numbers k such that w(k + w(k)) = w(k), where w(k) is the binary weight of k, A000120(k).
0
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.
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
KEYWORD
nonn,base,easy
AUTHOR
Ctibor O. Zizka, Apr 02 2022
STATUS
approved