

A329852


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


1



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

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 JeanFrançois 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



