Find the next number in the following series:
11, 12, 20, 23, 33, 46, ?, ?
The sequence is created by writing the Fibonacci initiating with the 5th term in progressive number bases starting with the binary number system.
Thus, denoting F(n) as the nth term of the Fibonacci sequence, we have:
F(5) = 3 => 11 in binary ( base 2) number system.
F(6) = 5 => 12 in ternary (base 3) number system.
F(7) = 8 => 20 in quaternary (base 4) number system.
F(8) = 13 => 23 in quinary (base 5) number system.
F(9) = 21 => 33 in senary (base 6) number system.
F(10) = 34 => 46 in septenary (base 7) number system.
F(11) = 55 => 67 in octal (bade 8) number system.
F(12) = 89=> 108 in nonary (base 9) number system.
Consequently, the required missing numbers are 67 and 108.
Edited on May 23, 2022, 7:45 am
Puzzle Solution
