In the following sequence, consisting of positive integers, the first term is a one digit number.
?, ? , 65, 61, 37, 58, 89, 145, ...
A) What is the first term?
B) What is the next term that is a one digit number?
The sequence is the sum of the squares of the digits of the previous term (Sloane A008463).
Except that we are given that the first term of the sequence is a single digit, there are many possible numbers that could begin the sequence:
33 => 32+32 = 18 => 12+82 = 65...
57 => 52+72 = 74 => 72+42 = 65...
75 => 72+52 = 74 => 72+42 = 65...
90 => 92+02 = 81 => 82+12 = 65...
744 => 72+42+42 = 81 => 82+12 = 65...
1136 => 12+12+32+62 = 47 => 42+72 = 65...
...
As it is, the sequence of condition begins with:
9 => 92 = 81 => 82+12 ... and, as given: 65, 61, 37, 58, 89, 145, then continues ...
=> 12+42+52 = 42 => 42+22 = 20 => 22+02 = 4 ...
Where, following, with the reversal of digits of the number found toward the beginning of the sequence, i.e., 61 reversed is 16, begins a repeated cycle: 16, 37, 58, 89, 145, 42, 20, 4. The 4, then, is the next and only other (repeatedly) single digit number of the sequence.
Edited on November 5, 2008, 10:19 am
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Posted by Dej Mar
on 2008-11-05 09:10:09 |
solution
