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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 :)