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.
%I A382053 #14 Mar 15 2025 11:31:04
%S A382053 0,1,2,3,4,5,6,7,8,9,10,12,13,16,19,20,22,30,33,46,47,56,85,105,109,
%T A382053 150,173,254,266,279,413,416,444,624,651,690,713,746,1031,1110,2841,
%U A382053 2864,2867,2892,2895,2994,4516,4523,4543,4559,7452,7491,7532,11840,11852,11863,19297,19311,19442,19462
%N A382053 Numbers k such that Fibonacci(k) has a Fibonacci number of 1's in its binary representation.
%C A382053 Numbers k such that A000045(k) is in A381704.
%e A382053 a(11) = 10 is a term because Fibonacci(10) = 55 = 110111_2 has 5 1's in its binary representation, and 5 = Fibonacci(5) is a Fibonacci number.
%p A382053 isfib:= n -> issqr(5*n^2+4) or issqr(5*n^2-4);
%p A382053 filter:= n -> isfib(convert(convert(combinat:-fibonacci(n),base,2),`+`)):
%p A382053 select(filter, [$0..20000]);
%t A382053 Select[Range[0,20000],ResourceFunction["FibonacciQ"][Total[IntegerDigits[Fibonacci[#],2]]]&] (* or if ResourceFunction Add-on is not available *) Select[Range[0, 20000],AnyTrue[Sqrt[5 #^2 + 4 {-1, 1}] &[DigitSum[Fibonacci[#], 2]],IntegerQ] &] (* _James C. McMahon_, Mar 14 2025 *)
%Y A382053 Cf. A000045, A381704.
%K A382053 nonn,base
%O A382053 1,3
%A A382053 _Robert Israel_, Mar 13 2025