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A221158 Fibonacci numbers with two 1's in the binary representation. 3
3, 5, 34, 144 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)