# Can you fill in the gaps in this number sequence?

The number sequence is

73, 70, 49, 52, 35, ?, ?, ?, ?, ?, 72,.....


Can you fill in the gaps and predict what happens after 72?

I have updated the hints below.

Hint 1

What are the factors of each number? Calculate factors for each number!

Hint 2

This is a mathematical problem, but does not require complicated maths

Hint 3

If a sequence using exactly the same mathematical rules is started with a different number a different pattern develops. For example; [ 1, 1, 1, 1, ........ ] and [ 48, 48, 48, 48, ........]

The 5 missing values are:

24, 12, 3, 9, 81

After 72:

Each subsequent value will be 9 less until it gets to 9, then start over at 81, repeating forever.

The method:

To calculate the next value, add the digits of the current value and multiply by the first digit of the current value.

• Great Job - Well done :-)
– tom
Mar 2, 2018 at 23:47

The gaps:

34, 21, 16, 7, 0

Reasoning:

Every other number is in octal. When converted to decimal, the values would be:
73, 56, 49, 42, 35, 28, 21, 14, 7, 0
Which (after 73) is of course multiples of 7 descending

I think the 73, 72, is another countdown. The first number in each sub-sequence is the largest multiple of 7 less than octal 73 or octal 72, etc.

So the sequence will continue...

73, 70, 49, 52, 35, 34, 21, 16, 7, 0
72, 70, 49, 52, 35, 34, 21, 16, 7, 0
71, 70, 49, 52, 35, 34, 21, 16, 7, 0
70, 61, 42, 43, 28, 25, 14, 7, 0
(Sub-sequence has shifted left and octal/decimal values are flipped)

• Nice reasoning and ideas, but very sorry this is not correct....
– tom
Mar 1, 2018 at 23:45
• ...you are correct to be working along mathematical lines, but I am afraid that this particular approach is not correct
– tom
Mar 1, 2018 at 23:47
• The idea of every other number in octal giving the sequence is brilliant, but sadly not correct.... --- so +1 for a great idea, but sorry not the correct approach
– tom
Mar 1, 2018 at 23:50
• @tom haha, thank you :) no need to apologize Mar 1, 2018 at 23:55