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

3, 5, 34, 144

Offset: 1

Author

Alex Ratushnyak, Feb 20 2013

Keywords

• nonn
• full
• fini

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

Examples

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

Links

• Noam D. Elkies, Fibonacci numbers with Hamming weight 2, Mathoverflow, 2014.

Crossrefs

Cf. A000045, A004685, A222296.

Programs

Mathematica

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

Python

from sympy import fibonacci
print([f for n in range(100) if (f := int(fibonacci(n))).bit_count() == 2]) # David Radcliffe, Jul 03 2025

Extensions

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