A220115 a(n) = A000120(n) - A007895(n), the number of 1's in binary expansion of n minus the number of terms in Zeckendorf representation of n.

0, 0, 0, 1, -1, 1, 0, 1, 0, 0, 0, 1, -1, 2, 1, 2, -1, -1, 0, 0, -1, 2, 1, 2, 0, 0, 1, 1, 0, 2, 1, 2, -2, -2, 1, 1, 0, 1, 0, 2, -1, 0, 1, 1, 0, 1, 0, 3, -1, 0, 0, 0, 0, 0, 0, 4, 1, 2, 2, 2, 2, 2, 2, 4, -2, -1, -1, -1, 0, 0, 0, 1, -2, 0, -1, 0, 1, 1, 1, 2, -2

Offset: 0

Author

Alex Ratushnyak, Dec 05 2012

Keywords

• base
• sign
• easy

Examples

			a(4) = A000120(4) - A007895(4) = 1 - 2 = -1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000120, A007895.

Programs

Mathematica

zeck = DigitCount[Select[Range[0, 500], BitAnd[#, 2*#] == 0&], 2, 1]; DigitCount[Range[0, Length[zeck]-1], 2, 1] - zeck (* Jean-François Alcover, Jan 25 2018 *)

Formula

a(n) = A000120(n) - A007895(n).