A221158 Fibonacci numbers with two 1's in the binary representation.

3, 5, 34, 144

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: A354849 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