A220116 -id:A220116 - cp's OEIS frontend

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

Alex Ratushnyak, Nov 22 2019

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

			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.

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

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 *)

A329853 Numbers having twice as many terms in their Zeckendorf expansion as 1's in their binary expansion.

Original entry on oeis.org

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

Alex Ratushnyak, Nov 22 2019

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

			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.

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

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 *)

cp's OEIS Frontend

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

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