|
%I #22 Apr 03 2022 09:56:47
%S 0,1,3,10,11,18,19,22,23,25,34,35,38,39,41,49,53,54,66,67,70,71,73,81,
%T 85,86,97,101,102,110,116,117,119,130,131,134,135,137,145,149,150,161,
%U 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
%N Numbers k such that w(k + w(k)) = w(k), where w(k) is the binary weight of k, A000120(k).
%C w(k + w(k)) - w(k) = 0 this sequence, w(k + w(k)) - w(k) = 2 for k = 4*j, where A000120(j) = 3.
%F k : A000120(A092391(k)) = A000120(k); A348367(k) = A000120(k).
%e k = 18; A000120(18 + A000120(18)) = A000120(18), thus k = 18 is a term.
%t w[n_] := DigitCount[n, 2, 1]; Select[Range[0, 300], w[# + w[#]] == w[#] &] (* _Amiram Eldar_, Apr 02 2022 *)
%o (Python)
%o def w(n): return bin(n).count("1")
%o def ok(n): wn = w(n); return w(n + wn) == wn
%o print([k for k in range(274) if ok(k)]) # _Michael S. Branicky_, Apr 02 2022
%Y Cf. A000120, A092391, A348367.
%K nonn,base,easy
%O 1,3
%A _Ctibor O. Zizka_, Apr 02 2022
|
