Irregular table of conjectured Fibonacci numbers with exactly n bits set in their binary representation.
1, 1, 2, 8, 3, 5, 34, 144, 13, 21, 89, 610, 2584, 55, 233, 4181, 377, 10946, 46368, 75025, 1597, 987, 6765, 17711, 832040, 121393, 2178309, 39088169, 28657, 196418, 317811, 1346269, 9227465, 514229, 5702887, 14930352, 63245986, 4807526976, 3524578, 2971215073
1
The known terms are in A222296.
T. D. Noe, Plot of first 1000 rows
T. D. Noe, Terms in the first 1000 rows
The irregular table is conjectured to begin
{1, 1, 2, 8},
{3, 5, 34, 144},
{13, 21},
{89, 610, 2584},
{55, 233, 4181},
{377, 10946, 46368, 75025},
{1597},
{987, 6765, 17711, 832040},
{121393, 2178309},
{39088169},
{28657, 196418, 317811, 1346269, 9227465},
{514229, 5702887, 14930352, 63245986, 4807526976},
{3524578, 2971215073}
(Mma) f = Fibonacci[Range[10000]]; Table[Select[f, Total[IntegerDigits[#, 2]] == n &], {n, 20}]
Cf. A004685 (Fibonacci numbers in binary), A221158 (two bits set), A222295.
Cf. S000059 (similar, but with Lucas numbers).
nonn,tabf
T. D. Noe, May 18 2014