cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A221158 #37 Jul 03 2025 10:57:16
%S A221158 3,5,34,144
%N A221158 Fibonacci numbers with two 1's in the binary representation.
%C A221158 Fibonacci numbers of the form 2^a + 2^b, a>b.
%C A221158 Elkies (2014) proved that there are no other terms.
%C A221158 This sequence is one row of A222296. - _T. D. Noe_, Mar 08 2013
%H A221158 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 A221158 144 = 128 + 16 = 2^7 + 2^4, thus it is in the sequence.
%t A221158 Select[Fibonacci[Range[1000]], DigitCount[#, 2, 1] == 2 &] (* _Alonso del Arte_, Feb 21 2013 *)
%o A221158 (Python)
%o A221158 from sympy import fibonacci
%o A221158 print([f for n in range(100) if (f := int(fibonacci(n))).bit_count() == 2]) # _David Radcliffe_, Jul 03 2025
%Y A221158 Cf. A000045, A004685, A222296.
%K A221158 nonn,full,fini
%O A221158 1,1
%A A221158 _Alex Ratushnyak_, Feb 20 2013
%E A221158 full, fini keywords added by _Max Alekseyev_, May 13 2014