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%I #29 May 08 2021 08:36:27
%S 0,2,5,13,55
%N Fibonacci numbers with only one 0 in the binary representation.
%C Conjecture: the sequence is finite.
%C No more terms below 2*10^301. - _Matthew House_, Sep 06 2015
%C 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
%e 55 is 110111 in binary, thus 55 is in the sequence.
%t Select[Fibonacci@ Range[0, 120], Last@ DigitCount[#, 2] == 1 &] (* _Michael De Vlieger_, Sep 07 2015 *)
%o (Python)
%o def count0(x):
%o c = 0
%o while x:
%o c+= 1 - (x&1)
%o if c>1:
%o return 2
%o x>>=1
%o return c
%o prpr, prev = 0,1
%o TOP = 1<<12
%o print(0, end=',')
%o for i in range(1,TOP):
%o if count0(prpr)==1:
%o print(prpr, end=',')
%o if (i&4095)==0:
%o print('.', end=',')
%o prpr, prev = prev, prpr+prev
%Y Cf. A004685, A221158.
%Y Intersection of A030130 and A000045.
%K nonn,base,more
%O 1,2
%A _Alex Ratushnyak_, Mar 08 2013
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