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

0, 2, 5, 13, 55

Offset

1,2

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

Links

Table of n, a(n) for n=1..5.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A004685, A221158.

Intersection of A030130 and A000045.

Sequence in context: A353722 A105905 A236513 * A075738 A076999 A360507

Adjacent sequences: A214850 A214851 A214852 * A214854 A214855 A214856

Keyword

nonn,base,more

Author

Alex Ratushnyak, Mar 08 2013

Status

approved