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A329852
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Numbers having twice as many 1's in their binary expansion as terms in their Zeckendorf expansion.
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1
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3, 5, 15, 23, 29, 34, 39, 57, 58, 60, 90, 92, 95, 102, 111, 125, 126, 144, 147, 149, 159, 165, 178, 183, 207, 237, 243, 249, 267, 335, 343, 390, 399, 413, 414, 432, 435, 437, 447, 467, 469, 474, 495, 500, 503, 612, 619, 621, 633, 634, 636, 667, 670, 686, 700
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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The binary expansion of 15, "1111", contains four 1's, and the Zeckendorf expansion contains two terms: 15 = 13 + 2. There are twice as many 1's in the binary expansion, so 15 is in the sequence.
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MATHEMATICA
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Position[DigitCount[(v = Select[Range[10^4], BitAnd[#, 2#] == 0 &]), 2, 1] / DigitCount[Range @ Length[v], 2, 1], _?(# == 1/2 &)]//Flatten (* Amiram Eldar, Jan 12 2020 after Jean-François Alcover at A007895 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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