

A329853


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


1



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
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OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..50.


EXAMPLE

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.


MATHEMATICA

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 JeanFrançois Alcover at A007895 *)


CROSSREFS

Cf. A000045, A000120, A007895, A220116, A329852.
Sequence in context: A034713 A101653 A043100 * A078714 A292208 A104125
Adjacent sequences: A329850 A329851 A329852 * A329854 A329855 A329856


KEYWORD

nonn,base


AUTHOR

Alex Ratushnyak, Nov 22 2019


STATUS

approved



