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A214852
Indices of Fibonacci numbers with the same number of 1's and 0's in their binary representation.
3
3, 36, 42, 59, 116, 156, 168, 211, 237, 246, 280, 335, 355, 399, 404, 416, 433, 442, 569, 580, 652, 698, 761, 770, 865, 897, 940, 989, 1041, 1049, 1101, 1144, 1214, 1286, 1335, 1352, 1369, 1395, 1698, 1726, 1810, 1928, 1940, 1951, 2055, 2159, 2326, 2332
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.
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