A329853 Numbers having twice as many terms in their Zeckendorf expansion as 1's in their binary expansion.
4, 16, 33, 72, 80, 129, 130, 132, 192, 258, 260, 264, 321, 513, 517, 528, 544, 608, 640, 768, 800, 896, 1025, 1028, 1032, 1056, 1184, 1216, 1280, 1538, 1540, 1552, 1792, 2050, 2054, 2057, 2060, 2064, 2082, 2088, 2113, 2177, 2180, 2184, 2240, 2304, 2308, 2336, 2368, 2432
Offset: 1
Examples
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.
Programs
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Mathematica
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 *)
Comments