Cool modular arithmetic prob

For discussing Olympiad Level Number Theory problems
Almx26
Posts:5
Joined:Fri Aug 28, 2020 11:08 am
Contact:
Cool modular arithmetic prob
An infinite series of integers follows the following rule:
$a_{n+1}=2a_n +1$
Is there any $a_0$ for which every term of the series will be a prime number?

Asif Hossain
Posts:194
Joined:Sat Jan 02, 2021 9:28 pm

Re: Cool modular arithmetic prob

Almx26 wrote:
Wed Jun 02, 2021 8:35 am
An infinite series of integers follows the following rule:
$a_{n+1}=2a_n +1$
Is there any $a_0$ for which every term of the series will be a prime number?
Is there any recipe to cook prime numbers?
Hmm..Hammer...Treat everything as nail

Mehrab4226
Posts:230
Joined:Sat Jan 11, 2020 1:38 pm

Re: Cool modular arithmetic prob

Almx26 wrote:
Wed Jun 02, 2021 8:35 am
An infinite series of integers follows the following rule:
$a_{n+1}=2a_n +1$
Is there any $a_0$ for which every term of the series will be a prime number?
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré

Mehrab4226
Posts:230
Joined:Sat Jan 11, 2020 1:38 pm
$a_{n+1}=2a_n +1$
Is there any $a_0$ for which every term of the series will be a prime number?