A329852 Numbers having twice as many 1's in their binary expansion as terms in their Zeckendorf expansion.

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

Offset: 1

Author

Alex Ratushnyak, Nov 22 2019

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Crossrefs

Cf. A000045, A000120, A007895, A220116, A329853.

Programs

Mathematica

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 *)