A214853 Fibonacci numbers with only one 0 in the binary representation.

0, 2, 5, 13, 55

Offset: 1

Author

Alex Ratushnyak, Mar 08 2013

Keywords

• nonn
• base
• more

Comments

Conjecture: the sequence is finite.

No more terms below 2*10^301. - Matthew House, Sep 06 2015

No more terms below 10^162809483. (This number could easily be raised. Of the Fibonacci numbers less than 2^32 -- i.e., F(0) through F(47) -- F(10)=55 is the largest that has only one 0 in its binary representation, and of those not less than 2^32, the smallest one whose 32 least significant bits include fewer than 2 zero bits is Fibonacci(779038816), which exceeds 10^162809483.) - Jon E. Schoenfield, Sep 07 2015

Examples

			55 is 110111 in binary, thus 55 is in the sequence.
		

Crossrefs

Cf. A004685, A221158.

Intersection of A030130 and A000045.

Programs

Mathematica

Select[Fibonacci@ Range[0, 120], Last@ DigitCount[#, 2] == 1 &] (* Michael De Vlieger, Sep 07 2015 *)

Python

def count0(x):
    c = 0
    while x:
        c+= 1 - (x&1)
        if c>1:
            return 2
        x>>=1
    return c
prpr, prev = 0,1
TOP = 1<<12
print(0, end=',')
for i in range(1,TOP):
    if count0(prpr)==1:
        print(prpr, end=',')
    if (i&4095)==0:
        print('.', end=',')
    prpr, prev = prev, prpr+prev