cp's OEIS Frontend

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

%I A214853 #29 May 08 2021 08:36:27
%S A214853 0,2,5,13,55
%N A214853 Fibonacci numbers with only one 0 in the binary representation.
%C A214853 Conjecture: the sequence is finite.
%C A214853 No more terms below 2*10^301. - _Matthew House_, Sep 06 2015
%C A214853 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 A214853 55 is 110111 in binary, thus 55 is in the sequence.
%t A214853 Select[Fibonacci@ Range[0, 120], Last@ DigitCount[#, 2] == 1 &] (* _Michael De Vlieger_, Sep 07 2015 *)
%o A214853 (Python)
%o A214853 def count0(x):
%o A214853     c = 0
%o A214853     while x:
%o A214853         c+= 1 - (x&1)
%o A214853         if c>1:
%o A214853             return 2
%o A214853         x>>=1
%o A214853     return c
%o A214853 prpr, prev = 0,1
%o A214853 TOP = 1<<12
%o A214853 print(0, end=',')
%o A214853 for i in range(1,TOP):
%o A214853     if count0(prpr)==1:
%o A214853         print(prpr, end=',')
%o A214853     if (i&4095)==0:
%o A214853         print('.', end=',')
%o A214853     prpr, prev = prev, prpr+prev
%Y A214853 Cf. A004685, A221158.
%Y A214853 Intersection of A030130 and A000045.
%K A214853 nonn,base,more
%O A214853 1,2
%A A214853 _Alex Ratushnyak_, Mar 08 2013