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A214853 Fibonacci numbers with only one 0 in the binary representation. 2
0, 2, 5, 13, 55 (list; graph; refs; listen; history; text; internal format)
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<<20

print 0,

for i in range(1, TOP):

    if count0(prpr)==1:

        print prpr,

    if (i&4095)==0:

        print '.',

    prpr, prev = prev, prpr+prev

CROSSREFS

Cf. A000045, A004685, A221158.

Sequence in context: A112836 A105905 A236513 * A075738 A076999 A306827

Adjacent sequences:  A214850 A214851 A214852 * A214854 A214855 A214856

KEYWORD

nonn,base,more

AUTHOR

Alex Ratushnyak, Mar 08 2013

STATUS

approved

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Last modified April 18 11:03 EDT 2019. Contains 322209 sequences. (Running on oeis4.)