A329853 - OEIS

A329853

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

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 Jean-François Alcover at A007895 *)

CROSSREFS

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

Sequence in context: A374001 A101653 A043100 * A078714 A292208 A383926

Adjacent sequences: A329850 A329851 A329852 * A329854 A329855 A329856

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, Nov 22 2019

STATUS

approved