A196024 Odious Fibonacci numbers.

1, 2, 8, 13, 21, 55, 233, 1597, 4181, 28657, 121393, 196418, 317811, 1346269, 2178309, 3524578, 9227465, 165580141, 1134903170, 1836311903, 2971215073, 20365011074, 32951280099, 53316291173, 225851433717, 2504730781961, 6557470319842, 17167680177565, 27777890035288

Offset: 1

Author

Kausthub Gudipati, Sep 27 2011

Keywords

• nonn
• base

Comments

Intersection of A000069 (odious numbers) and A000045 (Fibonacci numbers).

The k-th Fibonacci number is odious for k = 1, 2, 3, 6, 7, 10, 13, 17, 19, 23, 26, 27, 28, 30, 31, 32, 33, 35, 41, 45, ...

The k-th odious number is a Fibonacci number for k = 1, 2, 5, 7, 11, 28, 117, 799, 2091, ...

Examples

			8 is a Fibonacci number that equals 1000 in binary, which contains one (odd number) 1.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A000120, A007088, A004685.

Programs

Maple

isA000069 := proc(n)
        type(wt(n),'odd') ;
end proc:
for n from 1 to 300 do
        F := combinat[fibonacci](n) ;
        if isA000069(F) then printf("%d,",F) ; end if;
end do: # R. J. Mathar, Oct 15 2011

Mathematica

Rest[Select[Fibonacci[Range[100]],OddQ[DigitCount[#,2,1]]&]] (* Harvey P. Dale, Oct 16 2011 *)