# What number should be next? (hints added) [closed]

1 2 3 4 5 10 13 22 103 □

Identify □

one more number added due to OEIS

hint 1 :

it is related with "Base" system like base-n (numeral system)

hint 2 :

103's next number is 4-digit number
ex) 1234

hint 3 :

this number sequence's end is next two more numbers. this is inevitable.
1 2 3 4 5 10 13 22 103 □ □(end)

• If the "10" above would have been "11", I would have had the answer Nov 28, 2018 at 8:51
• Is this a puzzle of your own devising, or does it come from somewhere else? Nov 28, 2018 at 11:02
• it's the former Nov 28, 2018 at 11:40
• @j3App , you are almost there Nov 28, 2018 at 14:10
• @blackdoggy Is it "6664","26656","26661"?
– Ajay
Dec 7, 2018 at 9:54

It's time to grasp at straws for a bit.

An OEIS search for the sequence as it is yields nothing;

BUT

when you convert the sequence from base 6, you get 1, 2, 3, 4, 5, 6, 9, 14, which yields exactly two results on OEIS. The next number of one is 24 and the next one of the other is 21.

So the next number may be

either 33 or 40.

EDIT: with the new number it becomes

1, 2, 3, 4, 5, 6, 9, 14, 39.

Oh, I got it. Maybe.

The differences between the numbers (in the ORIGINAL SEQUENCE) is 1, 1, 1, 1, 5 (ignore this part), 3, 9, 81. If the next number is 6561 ($$81^2$$) higher than the previous 103, the answer is 6664.

OR (attempt 3):

if you convert it from base SEVEN you get 1, 2, 3, 4, 5, 7, 10, 16, 52. The difference between these is 1, 1, 1, 1, 2, 3, 6, 36. Besides the first seemingly random ones, each difference (starting with 6) is the product of all of the previous differences. $$36*6*3*2 = 1296$$. $$1296 + 52 = 1348$$. Converting back into base 7 gives (possibly) $$3634$$ as the next number?!?

• i am sorry but using OEIS is not in my purpose so i added one more. Nov 28, 2018 at 12:51

Is it

23 ?

I don't know how the number is counted from 1 to 5 & 10 but then

1 2 3 4 5 10 13 22

5*3 = 15 - 2 = 13
5*4 = 20 + 2 = 22
5*5 = 25 - 2 = 23

Let me know if I am totally wrong or partially right :)

• You got only 2 loose connections to the pattern and based on that you provide an answer. I think it is a bit far-fetched. I could come up with many theories like this one... Nov 28, 2018 at 12:37
• OK, let me guess another one for the same. Nov 28, 2018 at 12:39
• i added one more number Nov 28, 2018 at 12:42
• Yes, I am checking based on it again, but this time I don't want to be wrong. So taking care of full equation Nov 28, 2018 at 12:50
• Down voters may be don't know I have given this answer before edit was made. Nov 30, 2018 at 13:02

1 2 3 4 5 10 13 22 177. The next number is 177

• Please explain why this is the answer. Nov 28, 2018 at 9:23