

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
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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 c0c1
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

Cf. A000045, A004685, A259407.
Sequence in context: A291213 A158301 A105758 * A113799 A072682 A158207
Adjacent sequences: A214849 A214850 A214851 * A214853 A214854 A214855


KEYWORD

nonn,base


AUTHOR

Alex Ratushnyak, Mar 08 2013


STATUS

approved



