I think I have the answer and I don't think this is a REAL numbers problem. 1, 5, 10, 25 and 50 are all U.S. currency coins. The next coin in sequence would be the 1 dollar coin which == 100. So the next number would be 100.

I could be wrong but I see no relations between the numbers otherwise.

My guess for the next number is 62.5, can you figure out why?

My guess is 76, from polynomial inerpolation -- a lousy method for this but I like it. Sloane says it's either 100 or 65.

I was unable to get 62.5.

My only guess is

1 x(5/1) =5 x2 =10 x(5/2) = 25 x2 =50 x(5/3) =83.3
[download]

In other words, a sequence of two stages:

• multiply by (5 divided by n++)
• multiply by 2

monarch,
The approach I used is that each term was being multiplied by some number. There were two patterns of multiples woven together. One pattern was constant - x 2. The other depends on the previous value (prev / 2).

1 x 5     = 5    # pattern 1, no prev value so start with 5
5 x 2     = 10   # pattern 2, constant
10 x 2.5  = 25   # pattern 1, prev value 5 / 2
25 x 2    = 50   # pattern 2, constant
50 x 1.25 = 62.5 # pattern 1, prev value 2.5 / 2
[download]

Cheers - L~R

Hi Anonymous Monk,

I will go with 50 :-)

However, I also like the answer given by sulfericacid in Re: A script to determine the next number in a sequence. But as Limbic~Region said in Re: A script to determine the next number in a sequence: “For a given number of integers in a sequence, there are an infinite number of "formulas" that could produce that sequence.” This is why for your small dataset more than one answer is possible.

Cheers

lin0

Update: Added quote by Limbic~Region in attention to his comment in Re^2: A script to determine the next number in a sequence

lin0,
Actually, what I said is that are an infinite number of "formulas" that can produce any given sequence if that sequence is not complete.

Cheers - L~R

Start with something like this:

sub nextelt { @s = @_; use LWP::Simple; $q = join("%2c", map int, @s);
+ $d = get("http://www.research.att.com/~njas/sequences/?q=$q&n=1&fmt=
+3"); $s = join(",",@s); for $t ("VWX", "STU") { $l = ",".join(",", $d
+ =~ /^%[$t]\s+\S+\s+(.*)/mg); $l =~ /$s,(-?\d+)/ and return $1; } } 
warn nextelt(5, 14, 42, 132, 429, 1430);
[download]