View Full Version : What is the next number
efi107
Apr 28, 2009, 11:01 PM
What is the next number in this series?
1 , 2 , 6 , 42 , 1806...
Capuchin
Apr 29, 2009, 12:53 AM
2 possible answers are 3263442 and 3270666
Unknown008
Apr 29, 2009, 10:00 AM
I found that the next numbers have been multiplied by prime numbers... first;y by 2, then 3, then 7, then 43
And the answer of Cap, by 1807 and the other possibility, 1811 (which by the way is the next prime number)
3 is the 2rd prime number;
7 is the 3rd prime number including the 3rd prime;
But 43 isn't the 7th prime number after 7 inclusive... but the 11th..
That is quite confusing. Am I on the right track?
Perito
Apr 29, 2009, 10:11 AM
I found Capuchin's first value using this logic.
value_{n+1}=value_n\, \times\, value_n\, +\, value_n
The second value is 1 \times 1+1 = 2
6 = 2 \times2+2
42 = 6 \times 6+6
1806 = 42 \times 42+42
3263442 = 1806 \times 1806+1806
I'm not sure of Capuchin's other possibility.
Capuchin
Apr 30, 2009, 03:15 AM
Jerry, you're close to my logic, which was a(n) = a(n-1)*(next prime higher than a(n-1))
And Perito hit the logic behind my first answer, a(n) = a(n-1)^2+a(n-1)
Unknown008
Apr 30, 2009, 07:08 AM
Aha! Thanks Cap :)