|
%I #29 Dec 07 2019 12:18:26
%S 3,5,34,144
%N Fibonacci numbers with two 1's in the binary representation.
%C Fibonacci numbers of the form 2^a + 2^b, a>b.
%C Elkies (2014) proved that there are no other terms.
%C This sequence is one row of A222296. - _T. D. Noe_, Mar 08 2013
%H Noam D. Elkies, <a href="http://mathoverflow.net/questions/159142/hamming-weight-of-fibonacci-numbers/159144#159144">Fibonacci numbers with Hamming weight 2</a>, Mathoverflow, 2014.
%e 144 = 128 + 16 = 2^7 + 2^4, thus it is in the sequence.
%t Select[Fibonacci[Range[1000]], DigitCount[#, 2, 1] == 2 &] (* _Alonso del Arte_, Feb 21 2013 *)
%o (Python)
%o prev = 0
%o curr = 1
%o for n in range(3000000):
%o c = 0 # count 1's
%o p = 1
%o while p<=prev:
%o c += ((prev & p) > 0)
%o if c>2:
%o break
%o p += p
%o if n&1023==0:
%o print '.',
%o if c==2:
%o print prev,
%o prev, curr = curr, prev+curr
%Y Cf. A000045, A004685, A222296.
%K nonn,full,fini
%O 1,1
%A _Alex Ratushnyak_, Feb 20 2013
%E full, fini keywords added by _Max Alekseyev_, May 13 2014
|
