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Numbers having twice as many terms in their Zeckendorf expansion as 1's in their binary expansion.
1

%I #18 Feb 23 2020 17:10:11

%S 4,16,33,72,80,129,130,132,192,258,260,264,321,513,517,528,544,608,

%T 640,768,800,896,1025,1028,1032,1056,1184,1216,1280,1538,1540,1552,

%U 1792,2050,2054,2057,2060,2064,2082,2088,2113,2177,2180,2184,2240,2304,2308,2336,2368,2432

%N Numbers having twice as many terms in their Zeckendorf expansion as 1's in their binary expansion.

%C Numbers k such that A007895(k) = 2 * A000120(k).

%e The binary expansion of 800, "1100100000", contains three 1's, and the Zeckendorf expansion contains six terms: 800 = 610 + 144 + 34 + 8 + 3 + 1. There are twice as many terms in the Zeckendorf expansion, so 800 is in the sequence.

%t Position[DigitCount[(v = Select[Range[10^5], BitAnd[#, 2#] == 0 &]), 2, 1] / DigitCount[Range @ Length[v], 2, 1], _?(# == 2 &)]//Flatten (* _Amiram Eldar_, Jan 12 2020 after _Jean-François Alcover_ at A007895 *)

%Y Cf. A000045, A000120, A007895, A220116, A329852.

%K nonn,base

%O 1,1

%A _Alex Ratushnyak_, Nov 22 2019