

A221158


Fibonacci numbers with two 1's in the binary representation.


3




OFFSET

1,1


COMMENTS

Fibonacci numbers of the form 2^a + 2^b, a>b.
Elkies (2014) proved that there are no other terms.
This sequence is one row of A222296.  T. D. Noe, Mar 08 2013


LINKS

Table of n, a(n) for n=1..4.
Noam D. Elkies, Fibonacci numbers with Hamming weight 2, Mathoverflow, 2014.


EXAMPLE

144 = 128 + 16 = 2^7 + 2^4, thus it is in the sequence.


MATHEMATICA

Select[Fibonacci[Range[1000]], DigitCount[#, 2, 1] == 2 &] (* Alonso del Arte, Feb 21 2013 *)


PROG

(Python)
prev = 0
curr = 1
for n in range(3000000):
c = 0 # count 1's
p = 1
while p<=prev:
c += ((prev & p) > 0)
if c>2:
break
p += p
if n&1023==0:
print '.',
if c==2:
print prev,
prev, curr = curr, prev+curr


CROSSREFS

Cf. A000045, A004685, A222296.
Sequence in context: A222484 A222630 A187993 * A068111 A162444 A305858
Adjacent sequences: A221155 A221156 A221157 * A221159 A221160 A221161


KEYWORD

nonn,full,fini


AUTHOR

Alex Ratushnyak, Feb 20 2013


EXTENSIONS

full, fini keywords added by Max Alekseyev, May 13 2014


STATUS

approved



