OFFSET
1,1
COMMENTS
Conjecture: the sequence is infinite.
The sequence of Fibonacci numbers with the same number of 1's and 0's in their binary representation begins: 2, 14930352, 267914296, ... = A259407.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..400
EXAMPLE
Fibonacci(36) = 14930352 = 111000111101000110110000_2, twelve 1's and twelve 0's, therefore 36 is in the sequence.
MATHEMATICA
fQ[n_] := Module[{f = IntegerDigits[Fibonacci[n], 2]}, Count[f, 0] == Count[f, 1]]; Select[Range[3000], fQ] (* T. D. Noe, Mar 08 2013 *)
PROG
(Python)
def count10(x):
c0, c1, m = 0, 0, 1
while m<=x:
if x&m:
c1+=1
else:
c0+=1
m+=m
return c0-c1
prpr, prev = 0, 1
TOP = 1<<16
for i in range(1, TOP):
if count10(prev)==0:
print i,
prpr, prev = prev, prpr+prev
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Alex Ratushnyak, Mar 08 2013
STATUS
approved