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

1,1

Comments

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

Links

Table of n, a(n) for n=1..55.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A210111 A121219 A113732 * A283908 A284409 A006977

Adjacent sequences: A329849 A329850 A329851 * A329853 A329854 A329855

Keyword

nonn,base

Author

Alex Ratushnyak, Nov 22 2019

Status

approved