22 Apr '08 14:47>
Originally posted by forkedknightCORRECT!
479, the 72nd prime number after 71
Counting by primes:
1
3
(skip 1 prime number)
3
13
(skip 3 prime numbers)
13
71
(skip 13 prime numbers)
71
479
(skip 71 prime numbers)
Originally posted by mtthwThe pattern is also cubes of the natural numbers, how can one solution be chosen over the other.... ?
Reminds me of a problem I was once set at school. What comes next: 1, 8, 27, 64...
I gave 117. The difference between consecutive numbers is 7, 19, 37: the 4th, 8th and 12th prime numbers. So, of course, the next difference is the 16th prime number: 53.
Perfectly logical, and completely missing the obvious solution!
Originally posted by mtthwThere's a similar pattern with the squares of numbers:
Reminds me of a problem I was once set at school. What comes next: 1, 8, 27, 64...
I gave 117. The difference between consecutive numbers is 7, 19, 37: the 4th, 8th and 12th prime numbers. So, of course, the next difference is the 16th prime number: 53.
Perfectly logical, and completely missing the obvious solution!
Originally posted by forkedknightThe difference is that yours was the right solution - the difference between consecutive squares are consecutive odd numbers (easy enough to prove). In my case I came up with a completely different sequence that happened to coincide for the first few numbers.
right, they are all consecutive odd numbers
My point was I did something similar to mattw in school given the sequence of squares.