Hey Geniuses! Math problem...

[Mr.Domains]

Okay, I know there are some REALLY brainy people on here, and this kind of thing makes my brain ache, (I'm a programmer, but more on the creative side than with numbers).

I need an equation to generate a Math Pattern, (probably a fairly simple one, but not immediately recognizable like 2,4,6,8... or 10,20,30,40...).

I need a pattern that starts:

10, around (14-18), around (22-25), around (30-40), then onwards exponentially...
(It shouldn't be an immediately obvious pattern to joe average though...) :?:

 

[Mr.Domains]

I quite like this pattern, (I just can't work out what the formula is)... :blush:

1. 10
2. 14 (prev + 4)
3. 19 (prev + 5)
4. 25 (prev + 6)
5. 32 (prev + 7)
6. 40 (prev + 8)
7. 49 (prev + 9)
8. 59 (prev + 10)
8. 70 (prev + 11)
10. 82 (prev + 12)
11. 95 (prev + 13)
12. 109 (prev + 14)

 

[Johnn]

x=10
y=4
While loop
result = x+y
y=y+1
x=result
End While Loop

 

[Skinny]

Edit: never mind, Johnn beat me to it.

I was trying to do a proper mathematical function f(x) = something; but I couldn't get it, but if you are using a programming language
you should be able to implement Johnn's solution which was more elegant than mine.

Skinny

 

[vital]

Hey,

I think it's a kind of recurrence, so it could be something like:

a[SUB]n+1 = [/SUB]a[SUB]n[/SUB] + k + n

init:

a[SUB]0 [/SUB]= 10
k = 4;

C snippet:

a = 10;
k = 4;
    
while( a < LIMIT )
    a += k++;

 

[Gerry]

I think this is the formula NASA uses to plot proper angles on spacecraft re-entering earth's atmosphere.

 

[Mr.Domains]

Thanks Johnn, Skinny, vital, Gerry and asfas - you guys are great!

I didn't realize how bad my math sucks until I tried to use it for more than just straightforward multiplication or division ... still, it has been 20 years since I left school,

I actually need it as an equation rather than a loop, because I need to be able to calculate what the Nth number would be, but another member (asfas) PM'ed me to say I could use:

y = (x*x + 5*x + 14) / 2

Looks about right, although I haven't tested it yet. Thanks for all your help!

 

[Johnn]

You cannot produce multiple results with just one equation.
What are you trying to do with: Excel or programming.
Be specific and we should be able to come up with the solution.

 

[Theo]

Just don't try to divide by zero because your computer will explode.

 

[vital]

It's called dynamic programming - you need previous results, but it's exactly what recurrences do.

a[SUB]0[/SUB] = 10, k = 4

a[SUB]1[/SUB] = a[SUB]0[/SUB] + k + 0 = 10 + 4 + 0 = 14
a[SUB]2[/SUB] = a[SUB]1[/SUB] + k + 1 = 14 + 4 + 1 = 19
a[SUB]3[/SUB] = a[SUB]2[/SUB] + k + 2 = 19 + 4 + 2 = 25
...
a[SUB]n+1 = [/SUB]a[SUB]n[/SUB] + k + n

The formula you posted is right, and code using the formula (y = (x*x + 5*x + 14) / 2)
produces sequence you wanted:

7
10
14
19
25
32
40
49
59
70
82

iterating x from 1 to 10.

 

[Mr.Domains]

You cannot produce multiple results with just one equation.

Of course you can, the result of "y" depends on "x", in this equation: y = (x*x + 5*x + 14) / 2

$x = 1; $y = 10;
$x = 2; $y = 14;

The formula you posted is right, and code using the formula produces sequence you wanted:

Cool, thanks!

Be specific and we should be able to come up with the solution.

I want to charge users an incrementing amount for upgrades, level 1 costs $10, level 2 costs $14, level 3 costs $19, and so on... ideally I'd even have the increments increase slightly more rapidly, (10, 16, 24-ish, etc if anyone cares to fine tune it), but this is close enough. Cheers!

(Unfortunately it's virtual credits, like forum $'s, not real cash!) :uhoh: