100, 200, 300, 301, 302, 303, 304, 309, 350, 351

What is the pattern in this series?

P.S. I do not know. Need creativity

RandInt(99,400,10)→L1

?

*The Silver Phantom welcomes you*

It sounds like a little of both.

It looks like it could be a cubic (or maybe quintuplet) equation, with 300-304 being the flattest part, 350-251 being a second 'plateau', and the tail ends being the sections with the sharpest slant.

It's not cubic; I just tried the calc's regression. *Maybe* it's a 5th degree or 7th degree etc. polynomial, but idk… I'm too lazy to try regression by hand.

Possibly, it could be rand.

fPart(1-min(ΔList(fPart(Ans{40014²,40692}/(2^31-{85,249

Where Ans is the seed.

That's the code for rand, maybe someone can run a brute force algorithm on WabbitEmu at like 900% speed and figure out what seed you would need for

RandInt(99,352,10)→L₁

To work, lol.

It might be two or more segments or equations strung together. I'm thinking that either it's every other number, or one of these:

100, 200, 300, 301, 302, 303, 304 | 309, 350, 351

(Exponential equation one) | (Equation 2)

100, 200, 300 | 301, 302, 303, 304 | 309 | 350, 351

(Dropping tail of a cubic or greater equation)| [Stable/ constant section]|[Increasing] |[Stable/Constant]

Backwards, without zeroes, it reads:

153, 53, 93, 43, 33, 23, 13, 3, 2, 1

Dropping equation

How much more creative can we get?

*The Silver Phantom welcomes you*

First off, keep in mind that just because there is a pattern does not necessitate that it arises from a numerical function like a polynomial. Consider the following pattern:

135, 636, 786, 791, 292, …?

This obviously fits no numerical function. Maybe you can try to use an oscillating function like sin() or cos(), but that's not the most obvious pattern. Furthermore, given five points, you could say that this is a perfect fit for a quartic function, but again, that's not the most obvious pattern (the numbers will always be three digits). Besides, given *n* number of givens, you can always say that the pattern is a polynomial function of degree *n*-1, but that's just not how patterns are formed.

For this pattern, you move the right-most digit to the front, then increment the hundreds, tens, and ones places by 1, 2, and 3 respectively. For instance, 135 becomes 513 becomes (5+1)(1+2)(3+3) = 636. When a digit hits a number >9, then it just cycles the digit starting at 0. Finally, the numbers are *always* three digits long, even if the leading digit is 0.

The fact that this pattern goes from incrementing the hundreds place by 1 to incrementing the ones place by one indicates to me that this is not just a function of a sort. Finally, 309 and 350 seem to be key points.

Timothy Foster - @tfAuroratide

Auroratide.com - Go here if you're nerdy like me

Is it an easy pattern that doesn't need a calculator to figure out?

The interpolating polynomial is ninth-order with coefficients (exponent-descending)…

a = -901

b = 45999

c = -1015566

d = 12681774

e = -98221053

f = 485781471

g = -1517260544

h = 2832003396

i = -2762012016

j = 1084285440

…all over nine factorial.

I did some tinkering with the OP's subset and came up with: X+99min(X,3)+4int(11^min(X-8,1

But, the real answer is that their Roman numeral transliterations are alphabetically sorted.

This may not necessarily be a pattern, but if you write the numbers using roman numerals, the "letters" are all alphabetical.

ex. 304 > CCCIV , 309 > CCIX

But by this logic, 305 (CCCV) should also be in the series… This needs some more thought.

CalcKid, I am beginningt to understand now. But could you explain a little more, I'm still confused. Also, I need a refresher on roman numeral values (just like what is 50, what is 100, etc. I know how to read them if I know the symbols).