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Fibonacci numbers with both a prime number of 0's and a prime number of 1's in their binary representations.
0

%I #8 Apr 20 2021 06:59:39

%S 21,233,196418,9227465,165580141,2971215073,53316291173,2504730781961,

%T 3416454622906707,51680708854858323072,184551825793033096366333,

%U 898923707008479989274290850145,3210056809456107725247980776292056

%N Fibonacci numbers with both a prime number of 0's and a prime number of 1's in their binary representations.

%C 21 -> 10101, 233 -> 11101001, 196418 -> 101111111101000010,..

%t Select[Fibonacci[Range[6! ]],PrimeQ[DigitCount[ #,2,0]]&&PrimeQ[DigitCount[ #,2,1]]&]

%Y Cf. A000045, A144214.

%K base,nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 16 2010