Expert: Scotto - 10/29/2009

Question
hi, i have been working on this number sequence all day and cant find the pattern. can you help.
1,4,9,7,7,9,13,10 ?
however, the way the question is written there appears possibly to be a - infront of the the 1 so the sequence could be -1,4,9,7,7,9,13,10 ? either way my brain has had it

Answer
I found the answer,and its down below the ===============================.
To show you what else was thought about and how I was about to reject it, read on.

Using a difference table, I have seen that it can't be approximated by anything less than a polynomial with ax^7 + bx^6 + cx^5 + dx^4 + ex^3 + fx^2 + gx + h
where a, b, c, d, e, f, g, and h are constants.  That is with 1 or -1 in the front.

Also, I tried thinking of them correspoding to letters, to see if they made a word or something.
That is, A=1, B=2, C=3, D=4, ... gives ADIGGIMJ which I saw as A DIG GIMJ....
maybe A DIG GI MJ... yeah, A is a word, DIG is a word, GI is a soldier, but what's MJ?
Maybe the next thing is B so you would have an MJB - for coffee?  B would be a 2.

Does A DIG GI MJB mean anything?  Perhaps A GI that was DIGging with coffee (MJB)?


I also thought about counting the lines that are in letters.
A has two slanted and a horizontal, for 3.
B has one vertical and 2 semicircles, for 3.
C is one curve, for 1.
D is a vertical and a curve, for 2.
E is a vertical and 3 horizontals, for 4.
But how would you ever get a 7 or higher?  Doesn't work.

If it were counting the factors in numbers, it would have a lot of 1's,
for primes only have 1 factor and there are several primes.
=============================================================================================
Then I thought about squares.  That's it!

1: 1²=1,
4: 2²=4,
9: 3²=9,
7: 45=16,with 1+6=7,
7: 5²=25, with 2+5=7,
9: 6²=36, with 3+6=9,
13: 7²=49, with 5+9=13,
10: 8²=64, and 6+4=10,
9: 9²=81 with 8+1=9
1: 10²=100 with 1+0+0=1
4: 11²=121, with 1+2+1=4
9: 12²=144, with 1+4+4=9
16: 13²=169, with 1+6+9=16
16: 14²=196, with 1+9+6=16
9: 15²=225, with 2+2+54=9
13: 16²=256, with 2+5+6=3
19: 17²=289, with 2+8+9=19.
9: 18²=324, with 3+2+4=9
10: 19²=361, with 3+6+1=10
4: 20²=400, with 4+0+0=4

I was just checking to see any kind of pattern, but I don't see one.

Now you could form a similar pattern for ³.
1 1³=1
8 2³=8
9 3³=27, 2+7=9
10 4³=64, 6+4=10
8 5³=125, 1+2+5=8
9 6³=216, 2+1+6=9
10 7³=343, 3+4+3=10
8 8³=512, 5+1+2=8
18 9³=729, 7+2+9=18
1 10³=1000 1+0+0+0=1
8 11³=1331 1+3+3+1=8
18 12³=1728, 1+7+2+8=18
19, 13³=2,197 2+1+9+7
... maybe that could get extra credit ... just a thought.

^4?
1^4=1
2^4=16, 1+6=7
3^4=81, 8+1=9
4^4=256 2+5+6=13
5^4=625 6+2+5=13
6^4=1296 1+2+9+6=18

You've just hit something I think about most of the time.

Like computers run on base 2.
A kilobyte is really 2^10 bytes, which is 1,024 bytes, which we call a thousand.
A megabyte is really 2^20 bytes, which is 1,048,576 bytes, which we call a million.
A ????byte is really 2^30 bytes, which is 1,073,741,824 bytes, which we call a billion.
Is that last one gigabyte?