

A214853


Fibonacci numbers with only one 0 in the binary representation.


2




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



