Quote from: Gramas on January 06, 2016, 05:56:04 PM

Quote from: Bulista on January 06, 2016, 02:54:58 PM

Quote from: BurtW on January 06, 2016, 02:07:30 PM

Quote from: Bulista on January 06, 2016, 10:46:00 AM

-snip-

I think that what you have done is to pretty much prove it is random and there is no predictive formula.

I'm not sure.

I got some infos that are getting me to believe that there is a possible formula behind it.

I give you an example. I'm playing around by creating random formulas, and I get pretty much similar results. Yet they are predictable with a formula.

All I use for inputs are 2 arrays, one with the current position and another with the sequential list of prime numbers.

For example:

Consider n = count, p = prime numbers, and y = sequence based on the formula 2^n + (n mod p) * Log(n+1, 2) <--- Random formula I invented.

y / 2^p + 1 and y-2^p *-1 are similar formulas to what was shown before for the var x in the real sequence, their results also appear to be random...

n	p	y = 2^n + (n mod p) * Log(n+1, 2)	y / 2^p + 1	y-2^p *-1
0	2	1	1.25000000	3
1	3	3	1.37500000	5
2	5	7	1.22406016	25
3	7	14	1.10937500	114
4	11	25	1.01234752	2023
5	13	45	1.00548399	8147
6	17	81	1.00061679	130991

Yet this sequence is breakable with a simple formula.

EDIT: this formula doesn't make any sense I know, just playing around

Am I the only one noticing that this guy makes a random formula using prime numbers and his first 3 results are exactly the ones as the sequence for this puzzle?

It seems pretty obvious that there is some formula using prime numbers behind this, no? And possibly the formula he posted is not so far from the real one.

Keep up the good work all!

Yea, I was actually surprised by those 3 first results since I was genuinely trying random stuff.

Maybe with some tweaks we can get to the right formula, if there is indeed one Grin

One thing I'm sure if we stop looking we won't know.